I agree completely, this project is the blind leading the blind. Even if you do come up with something that works, it'll be by chance, and probably won't be working for the reason you think it is. You've not even mentioned grounding, which I strongly suspect is at the root of your problem.
A PC power supply switches at anything from 50kHz upwards, but that's before you consider by far the most important aspect of the noise which is the RF component of the switching spikes. The true noise bandwidth will extend from a few Hz (coming from the switching jitter and instability in the control loop) up to hundreds of MHz, and no single technique works across that entire range.
You need to know what noise is affecting the circuit, where it's coming from, and how it's coupling into the circuit in a way that actually affects its operation. Only then can you determine whether a filtered supply from the PC will even make any difference. Sorry to be blunt, but speculation and guesswork isn't going to solve this one quickly or easily.