Most of the 'over the counter' type computers come with very small wattage power supplies that wear out quickly trying to power up modern hardware. Powersupplies are relatively cheap so get at least a 450watt or higher....and they're easy to replace. Just make sure that you have the 'map' of the pin connections for the power led, reset, spkrs, etc. that all located together on the motherboard (usually down in one of the far corners).
While you have the case open, check for dirty fans and replace ones that can't be cleaned up with regular rubbing type alchohol and a q-tip swab. Also an inexpensive item.
Before you replace the powersupply, look at the back of the computer for an I/O (it's actually a 1/0) switch. Unplug the computer, and move that switch back and forth to where it is again in the correct position of having the "I" pressed down....then plug the computer back up and try the power switch again. I just recently had a computer that for some reason had reset itself out of the blue even though the switch hadn't changed position and also wouldn't power up. I tried that, and it turned on again and never gave the owner anymore problems after that, so you could get lucky.
Hi, my daughter has an Emachines T2596. According to her, it just failed to work when she pushed power button one day. I looked at it and observed the following; the power button is lit, as it should be. The fan ran sporadically on at least one attempt to make it boot. Other than that, it makes no other effort to start the boot process at all and makes no normal boot noises. Is it safe to infer the fan wore out and the power supply overheated and i need to replace both? Will the rest of the computer have been damaged if this is the case? Any help appreciated. Thx