95% likely to be a PSU problem. Get a PSU with equal wattage from Antec, Corsair, Seasonic, XFX, or another brand made by any of those companies and test it.
The agiler PSUs are impossible to find reviews for, nigh impossible to even find the stated wattage for, they have higher amps on the 3.3v and the 5v than they do on the 12vs, and extremely cheap.
That is like the 4 worst things possible to have in a PSU.
I would almost bet money that a good PSU would fix everything immediately.
- Edit - Trying the same PSU in a much worse PC isn't a good test of anything. The hardware in the newer PC and the stress from the Alice game puts much more demand on the PSU than a much older game running on much older hardware will (call this 99% likely). Either put the same PSU in a better PC and run a more stressful game on it or put a better PSU in the PC with the problems. Those are the only two tests that will rule out the PSU being the problem.
- Edit 2 - I just wanted to throw it out there that any time the PSU is an afterthought in a computer, its probably to blame for problems with the computer. In this case, the OP listed it last after things like RAM, Hard Drive, etc. Most people put things they think are more important toward the top of lists they make barring a good reason not to. Properly ranked a PSU should be at least one of the first 3 or 4 components in any component listing.