If there’s an LED coming on, then the power supply works - at least, well enough to power the LED.
An LED coming on (and maybe blinking) is a code for a variety of RAM/BootROM errors. Apple used to have a support note on this, but I don’t seem to be able to find it now. However, the University of Oregon has a reference:
UofO’s list of blink error codes matches my memory, and is as follows:
- Black screen, power LED on (solid): POST or BootROM failure
- Flashing power LED once per second: bad RAM or no RAM
- Three flashes, a pause, and three more flashes (occurs continuously): marginal RAM
If the LED is blinking, I’d try replacing the RAM. If you have no compatible replacement RAM, at least remove the RAM you have, clean off the contacts on the RAM sticks with a pink rubber eraser so they’re shiny, scrub out the RAM sockets with a soft dry toothbrush to get any gunk out of them, and try booting with the cleaned/reinstalled sticks.
It’s possible that one stick may have gone bad, while the others are still OK. Although installing in pairs is preferred for this generation, you can try each stick individually to isolate any stick that may have failed, and replace only the filed ones.
In the event that any of the followup commenters have a solid LED, the only way to repair the Boot ROM is to reinstall the operating system. You may need to reformat the internal drive as well, if the drive blocks where the old Boot ROM are physically damaged.
Your best bet is to boot from an external drive (hard drive or flash drive) with Disk Utility and an appropriate OS installer. Use Disk Utility to repair the internal drive first, then see if you can restart. If not, then try to reinstall the current OS. That will replace your damaged system software without altering your user account.
If that doesn’t work, then the safest thing is to boot from an external boot drive, clone your internal drive to a second external drive (using Carbon Copy Cloner or SuperDuper!), then erase (or reformat) the internal drive using Disk Utility, reinstall the operating system, and restore your applications/user accounts from your clone or from your last trustworthy Time Machine backup.
If you have a reliable and reasonably speedy broadband connection, it’s possible to boot your computer from an online Recovery Disk using keyboard shortcuts, and do repairs/OS reinstalls even if you don’t have an external boot drive. Different OSes can be reinstalled by different methods, depending on what OSes you’ve used before.