What you want is quite unlikely to work. Here's why, and what you can try if you wish to attempt to make it work, anyway.
Just moving the old HDD to the new machine has one major problem. The Windows OS installed on it already is "customized" in the sense that it has all the drivers needed for the devices in your old machine, and almost no others for other device types. Now, "device" is not merely added cards like sound chards or video cards. It includes all the "devices" built into your old mobo, like the HDD controller chips, any on-board sound chip, the USB controllers, and eSATA chip, etc., etc. There could be 50 of them! If you simply move the HDD to your new machine (I'm ignoring completely whether the HDD is older IDE or current SATA), when you first try to boot up, Windows will load all the drivers it has and then discover that it is using the WRONG drivers for some devices on the new mobo, and is completely missing some others it needs now. The usual result is a crash and failure to boot.
A few lucky people get the new machine to appear to boot this way, and then can go into Device Manager and repair all the wrong or missing drivers manually. Don't count on that!
There is a process you can use to TRY to fix this problem. If you do this, it is best to do it right from the start - that is, do NOT simply boot up and let it fail. WARNING: what comes next could fail AND damage data on the HDD so that you lose everything. So before you even start, do this on your OLD machine. Make a complete backup of your old HDD. Then VERIFY that the backup is good and can be read, and can be used to completely restore that HDD if it becomes corrupted. Only after you're confident you have all your old stuff backed up safely should you proceed.
OK, So if you're going to try this fix-up process, you need the old HDD installed in the new machine, AND you need your Windows Install CD in your optical drive, AND you need to go into BIOS and set it to boot first from the optical drive containing the Install CD. BUT you do NOT do a normal Install. Look in the starting menu for an option to do something like a Repair Install. This process will take an inventory of the actual devices present in the (new) machine, then of the drivers already on the old HDD, and try to fix the mismatches - get rid of old drivers not needed, and add all new drivers required. IF it works, the machine will be able to boot from the old HDD that has just been "upgraded" with proper drivers. You might still be in the situation that there are driver errors that you must find and fix manually in Device Manager, but that can be done.
The huge advantage of this process is that you actually can boot and run from the old HDD with your OS operating and all your applications software already installed, and all your data files present. A minor disadvantage if it DOES work is that you're working with a slightly messy "updated" OS and drivers. The big disadvantage is it may NOT work at all, and you still can't boot! In fact, your HDD now has been so changed that it probably won't work in your old system, either, and you will have to restore it from your backup.
The "right" way to do this is longer and a bit tedious, but it will work perfectly. However, it needs a second HDD. Option 1 is you need to place on that second HDD a complete copy (ideally, a clone) of your old HDD using your old PC. This clone copy may be temporary until you get your old HDD doing the whole job, and then you don't need the second HDD any more. Option 2 is, you buy a new HDD to become the boot drive of the new machine, and LATER install the old HDD in the new machine and copy over the data files. Then the old HDD simply is a second HDD for data storage.
So, with a clone copy of your old HDD on some other drive, you install your old HDD in the new machine as the boot unit, then do a completely fresh Install of Windows on it. As the first step, you tell the Install routine to Delete any and all Partitions it finds on the old HDD before proceeding. Note that you do NOT want to have any other HDD mounted in the new machine as you do the Windows Install. (This is to defeat a Windows safety feature that has caused problems for some - I'm skipping those details.)
Alternatively, if you buy a new boot drive for the new machine, just do the normal Windows Install on it.
When Windows has been fully installed, then you must Install ALL your applications software on the new machine. You cannot simply run apps from your old drive on the new machine. The new machine's fresh Windows will know NOTHING about those apps in its new Registry, so they need to be Installed to establish those Registry entries. Once that is done you can install the OLD HDD (or the temporary one containing the clone copy) in the new machine and copy all your old document files to the new C: drive. Then the temporary HDD can be removed (if that's how you did it.) Later, when you're SURE you copied everything you needed, you can wipe the temporary clone copy out. OR, if you used a new HDD for C and installed the old HDD as a second drive, you can wipe it clean by re-Partitioning and Formatting it, and start using it as a data drive.