Easiest thing to check for is heat, check the case and fans for dust. Check the motherboard for any capacitor issues, they should all be flat, if any are puffy or showing black dots or leaking, bad.
If those look OK, you should try a new power supply. And make sure your components don't exceed the wattage of the power supply if you added anything new to the PC.
How 'bout some more details regarding your computer? Some models are known to have issues similar to yours due to bad capacitors. I just had to replace a pair of caps on a Shuttle SN68SG2 for this very type of problem.