Ineedhelp: If you disconnect the IDE cable to your hard drive, then turn on the machine, will it boot up and display an error message? Try this several times and be sure you get the same error message consistently. If you get a different error message or response between boots, you can stop because the hard drive is likely ruled out of the problem. If it's the same message, let us know what it is, and we'll explore from there- that would likely indicate that the HD is failing.
Are there times when you press the power button and nothing happens? Or something way out of the ordinary happens (an extra beep, slow time for fans to power up, a cd drive flashing oddly, etc.)? This may point indicators towards the power supply.
Some modern bios's are coming with options to "scan the health" of your machine. It's not a great science yet, but it typically if it says there's a problem, it's accurate that one exists. (Whether or not it names the problem correctly is a different situation...) When your machine boots up, you'll typically see something on the screen saying "Press (del, esc, f1, tab) to enter setup." Do that. Then look around the menus there for something about scanning health. I don't know how familiar you are with the BIOS, the menu set this will get you to, but don't change any settings in there, yet, unless you know what you're doing. Just run the scan if you can find it, and let us know what happens. If you can't find it, DON'T CHANGE ANYTHING IN THERE! You could make things worse if you do.
As a final option, it's possible you might have some bad RAM. If you have more than one stick of RAM in your machine you might try removing one, booting up see if it works fine. If it does, reboot a few times be sure it continues to work. If not, replace stick #1, take out #2 and repeat the process as above.
If you're not comfortable doing something we suggested, don't do it until you ask for some help. It's typically not that hard, but on occasion you can make a mess of things if you do it wrong. We'll help you get through it- just ask.
Let us know exactly what you've tried, and what the results are, and we'll try to help you through this. Good luck!