There are a couple of options for you (we'll ignore the complicated ones). For starters, hard drives generally are compatible with all motherboards - well, at least most desktop motherboards can use most 3½" hard drives commonly used in such machines - so your problem is not likely to be a real "problem". But there are some tricks you will need to know to help it work smoothly.
The heart of this seems to be that you are forced to get a new computer because your old one failed on a few critical components. However, you want to have access to / keep using the stuff on the old machine's hard drive. That is perfectly reasonable and not hard to do. It will come down to two main options, with a few wrinkles to take care of.
FIRST consideration is the type of drive. From what I can see, your machine only was sold with an IDE type of hard drive. From what you say I suspect you have seen the inside of your old machine, maybe even still have it open. So here's how you check what your HDD type is. An IDE type has two cable connections to its back edge. One is called a 4-pin MOLEX. It comes from the power supply unit (PSU) and has 4 separate wires - red on one end, two black in the middle, yellow on the other end. The other is one molded connector with 40 holes in it (well, 39 because one is blocked off) on the end of a 2" wide "ribbon" that has 80 wires in it, and a red stripe along one edge. The connector on the end of the ribbon, probably the one into your old HDD, is black. There may be another one of gray color in the middle of the ribbon cable, but maybe not. The other end of the ribbon should have a blue connector on it that is plugged into the motherboard port.
A SATA drive has different connections. It power connector from the PSU has 15 pins in it and is on a ribbon cable, not on 4 individual wires. It data ribbon only has 7 wires in it (less than 1" wide), unlike the wide ribbon on the IDE drives, and it will NEVER have a third connector in the middle of it.
So, from that you should be able to confirm which type your old drive is. When you go to buy a new machine I fully expect it will have several motherboard connections available for SATA drives, and it will come with one SATA HDD unit installed, and probably an optical drive also on a SATA port. BUT if your old HDD is an IDE type, make SURE your new machine also has at least one IDE port on its motherboard, too. You can connect up to two IDE devices on one mobo IDE port (if you have one of those cables with three connectors on it, including a middle gray one), and the cable from your old machine will fit into the new machine along with your old HDD, even if your new machine does not come with its own IDE ribbon cable. ALSO make sure that the PSU of the new machine has a few of those 4-pin Molex power connectors coming out so you can use one for your old drive.
So here's your first option, and the easiest. You buy a new machine that has a hard drive already installed as part of it, and even includes the Windows OS installed on that HDD. You start it up, it works, and everything is fine. The small task, and easy, is how to get to using the old HDD's data files. But just before doing that, give a little thought into your old applications - things like Microsoft Office 7 suite, or the Firefox browser, or whatever you have been using for various tasks. If your new machine comes with those already installed on its hard drive (even if these are actually newer versions of the app software you had), you're OK. But if your new machine does NOT have some application installed that you used on your old machine, getting it to run from your old drive can be a little tricky sometimes. The easier solution IF you can do it, is to install that software from its original Installation CD on the new machine BEFORE you add in the old drive. When installed like this, the application just works so much more smoothly.
So, with that done, you shut down your machine and pull the power cord, and open it up. Check the jumpers on the back edge of the old HDD IF it is IDE type. (If it is SATA, do NOT change any of its jumpers even if there are some!) Check the diagram on the HDD label. I suspect you will find the jumpers are set to "CS", which is all right. (The alternative is for you to set to "Master".) Mechanically mount your old HDD in an empty slot for it. Connect up power and data cables. If it is IDE, plug into it the END (black) connector on the ribbon cable - it only will plug in turned the right way. If it is SATA, there is only one connector possible, anyway. Close up the case, connect the power cord.
Next step is to enter BIOS Setup and check a couple of settings. To do this on most machines you hold down the "Del" key when power is turned on and keep holding it down until a few screens go by and it stops on the BIOS opening menu screen. Usually there are tabs across the top you can choose, and on the right or at the bottom you will see prompts about how to move the highlight cursor and how to change things or set them. You need to find the place where the port for your old HDD is set up. If it is SATA and your machine's new drive also is SATA, I fully expect that all of the SATA ports will be Enabled already. But near there is a place to set the SATA Port Mode. IF you can set this separately for each SATA port, set the one that your old drive is plugged into as IDE (or PATA) Emulation. But if you can't set individually, do not change it - leave it alone so the system can handle your new drive properly.
On the other hand, if you old drive is IDE type, look in the BIOS menus for where the IDE ports are configured. Make sure they are Enabled. I expect everything else about them will already be set to the right thing. Now look for a menu where you specify the Boot Priority Sequence. Check what it set there. The best is probably to try the optical drive first, then the NEW drive that came mounted in your new machine, and NO mention of the old drive you just installed. From there just use the keys (maybe F10) to Save and Exit, and your machine should boot up normally. However, if you look in My Computer, you will see your old drive is now added in (probably called E: or something like that). All its files will be there to use. If you want, you can copy documents and data files from there to the matching folders in the new drive so you can find them in My Documents instead of having to look on a different drive. But you don't have to - any application software can find and use files anywhere in the system. The fact that you have an old Windows XP installed on the old drive will just be ignored in this configuration.
The second main option is if you plan to buy a new machine without any new hard drive or OS installed, and plan instead to use the old Windows XP already installed on the old HDD. This MIGHT work, although you will probably start running out of space quickly with only 40 GB. In this case you still will need to install the old HDD in the machine and, if it's IDE type, ensure its jumpers and cables are set up as above. Then you will have some adjusting to do to get it working.
The issue is NOT compatibility of hard drive with motherboard. The issue is drivers for hardware devices. Every machine has a whole bunch of "devices" in it, most of them actually part of the motherboard. Windows needs device drivers (little software units) for each of these. When Windows XP was first installed on your old computer, it also installed the exact device drivers for all the devices it found in that machine. But now when you place it in another machine it has a bunch of drivers on the old HDD for devices that are no longer present, and it does NOT have drivers for a bunch of new devices. Usually this means you cannot get Windows to load and run. There is a solution that usually works. Ideally you need the Windows Install Disk (CD) used to install Windows on that HDD in the first place. If you can't get that, some borrowed Install CD for the same version (in your case, Windows XP with the RIGHT Service Pack included) can be used. Put that CD in the optical drive. You must go into BIOS Setup as above and make sure that the Boot Priority Sequence does list the optical drive as the first choice, and the HDD as second, then Save and Exit. It will boot from the Install CD and start like an normal Install. BUT watch the first screens and, when you see the choices, do NOT do a normal Install - that would wipe out all your old stuff!. Instead do a Repair Install. This is a process that checks what hardware devices really are present, and which drivers are already on the boot drive, and tries to fix all of the mismatches. If it all works, your Windows will be able to boot from this patched old drive. As I said, this procedure is a little more complicated, and not quite so sure to work.
Let us know which way you chose to proceed, and any questions you still have before diving in.
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