One thing to point out: A bad hard drive
can cause a system to not power-up, though it is rare. I've seen it happen, and it's not fun figuring that one out, b/c you don't expect it. That is when it is causing electrical issues only, I believe, which again is pretty rare.
As for your issues, here's what I'd do:
1. Try a different monitor - if the screen isn't coming up, but fans spinning, lights, etc, then it could be the monitor - causing one problem anyway. If nothing still, it could be the graphics adapter, so if can swap that, then do.. otherwise, you can try the other options just to see..
2. Open the case and look for bad capacitors as is mentioned by rclarke250. Check closely to see if any are leaking. If they are, then whatever component has the leaky capacitors (usually the motherboard, but it could happen with anything that has capacitors) is toast or probably not worth fixing unless you also like to do soldering on motherboards.
3. Unplug the hard drive, and try turning the system on. If it'll at least give you some errors like no boot disk found or something, but will do more than with hard drive connected, then you can pretty well assume that IS the problem.
4. If that doesn't tell you for sure, try pulling out all but 1 stick of RAM/memory, assuming you have more than one. Try booting that way... and test all RAM sticks the same way.. if you find a problem stick of RAM, then that's the issue.
5. If no power at all, then it's more likely to be the power supply something from the wall, or bad capacitors on the motherboard - in the power area.. or CPU/Ram area..
.... IF YOU CAN GET PASSED THE SCREEN PART ....
As for the virtual memory changing, etc... it makes me wonder if you're running low on space, assuming Windows is managing the virtual memory...
IF you can get past all of that, then running a system cleanup utility or built-in cleanup might work. For instance, you could run CCleaner or Glary Utilities to tune/clean things up... but you've got some other work to do before you even get here.
Keep us posted.. maybe I'll remember to check back on the progress.
"But thanks be to God, which giveth us the victory through our Lord Jesus Christ." 1 Corinthians 15:57