The message that says "entering power saver mode"... thats from the monitor, right? Does anything else show up on the screen before that?
Assuming that nothing else shows up on the screen before that message, a dead stick of RAM could cause the computer not to POST (Power-On Self Test, the self-diagnostics run before the OS gets loaded). I'm assuming that you have either 2 or 4 sticks of RAM. Try removing one of the sticks of RAM then see if the computer works. If you have 3-4 sticks, try removing all of them then test the machine with 1 stick at a time. You could also try swapping another video card in there and see if that works.
Try not to build up any static electricity and also be sure touch something metal (like the computer case or a lamp) to discharge any you've built up before you touch the internal computer parts.
In my experience, dead power supplies tend to just die and stay dead, or lose power after a few minutes whenever you try to use them. There are power supply testers for as little as $10, but they only test for under and over-voltage.
A dead or dying system board tends to have different symptoms than what you've described, but could still be the problem. If you know your model of system board, you could find a manual for it online. You might have diagnostic LEDs on the board itself that can tell you where the problem is (video, RAM, etc). That has worked for me before.
