I'm sorry, there is a reason why most people will say that a reinstall should be done.
*Especially* for a malware infested computer. You will never know what the malware has done. You might be able to revert some of the more obvious things, but getting rid of malware completly can be quite difficult.
If you want to try, the first order of business should have been to *not* connect it to any network. Boot it from a rescue disk or USB stick to make an offline scan of the filesystem for malware. There are plenty free AVs out there that can create such a disc.
I would also generally question the integrity of the HDD. Those don't get better over time, even just laying around.
If there is important data on it (i would think not, otherwise why have it sitting around for ten years), then it *might* be worthwhile to investigate.
But even then, just copying the really important stuff off would be the utmost i would even try to do to such a machine.
Also, do not forget that a Windows 7 10 years ago is not all that comparable with a fully patched Windows 7. You will never get the same performance again, it will inevitably run slower, or at least feel slower, than it originally was. At least SP1 increased the hardware requirements a bit if i remember correctly, and most patches add bloat and slowness.
I am aware that i have a biased look at this. For quite some time i did desktop support for a living.
I also liked to look for root causes and fix those, but at the same time it is important to be aware of a lost cause. In those cases noone would pay for the time it would take for a graceful recovery. And as mentioned above, you can't even be sure to get fully rid of malware. A clean slate reinstall is just the only sensible way to go there.
If you are serious about using this machine, invest in a small SSD, since that will give you a *huge* performance boost, and reinstall Windows 7. It will feel like new.