First, use rescue disks or similar to return the new comp to its original state. Then, format the old PC and never use it again.
Seriously, the old PC needs to reformatted, or at least Windows on it re-installed. It does seem like there's a virus on it, and it's probably one that can hide itself. You should run a DOS-based anti-virus-program, like the F-Secure to make sure there's nothing on there.
And as for the new PC, if it doesn't work after the rescue, check your power supply. Even small spikes in the current can cause erratic behaviour in PC's. Also check for any grounding problems and finally, check that you RAM-modules are okay. You can find software on the net for this.
Ice