The varieties of "YES" here depend a little on the planned use, but Yes anyway.
IF you want to just move the old drive to a new machine that already has a boot drive known as C:, so you can access old files on that old drive, the answer certainly is Yes. The main question to consider, though , is that mentioned by alvine. It is MOST likely that your old unit has an IDE interface, so your new machine would need to have at least one IDE port to connect that to. When you do that, I assume that this unit will be the only device connected to that IDE port. So, check two things: (a) the drive's jumpers should be set to Master (or Master with No Slave Present, if that is a different setting); and, (b) it should be plugged into the END (Black) connector on the 80-conductor ribbon cable. After it is connected, boot into BIOS Setup and verify that the BIOS "sees" it correctly. Then go to where you set the Boot Priority Sequence and make sure this old unit is NOT one of the possible boot devices. Then Save and Exit. When you do it this way, your old drive will show up in My Computer as a drive you can use with its own letter name, ana all its files should be there to use. You cannot boot from it, but I've assumed you do not intend to.
On the other hand, IF your plan is to use this as your main HDD that you boot from, it gets a bit tricky. It is VERY likely that your new machine will NOT just boot from it if you just plug it in and try to start up. That old unit has all the drivers for devices in your old machine, and none of the drivers for the new machine, so it cannot use the devices and boot properly. In SOME cases there is a process to update all the drivers, but that may not work in your case. IF this is your plan, post here and we can try to advise more details.
The third option is: do you plan to wipe this old drive clean and start with a fresh install of some version of Windows on it, so that it becomes the boot drive of the new machine? If you do, that can be done. However, that means losing all the files on it, so you will need a complete backup before starting. Also consider that 80 GB is considered pretty small in today's world, and the HDD is over 12 years old, so its reliability may be in question. For both these reasons, a new HDD might be a better choice.