My first thought with this would be faulty RAM or possible debris in the RAM slots on the logic board. This would be my approach to the problem.
1) I would attempt to remove the RAM and inspect the RAM slots on the logic board, using compressed air and/or a small pick if debris is visible.
2) Reset the SMC. A lot of odd issues can come back to a faulty SMC state, which are often resolved by resetting it. You can do this using the following steps, you might see the power adapters LED change color during the process.
- Connect your power adapter to your computer and ensure that your Mac is turned off
- Hold the (left) Shift, Control and Option keys and press the power button for 3-5 seconds
- Release the power button and all of the keys at the same time
- Press the power button to turn on the Mac
3) If you remove both RAM DIMMs and attempt to power on the Mac does it beep (different from the normal chime) at all or is it just a black screen with with only the fan spinning? If the Mac doesn't beep then it's failing to recognize that no RAM is installed, which it checks during it's boot process. This tells us that it's not progressing past the early stages of the boot process. If this is the case then you can try disconnecting components (hard drive, optical drive, display, etc) and then powering on again. If it eventually chimes or beeps then you can start reconnecting components, knowing that once you connect something and stops working then you have found the failure.
Also, are you sure that it's booting? For instance, if you power it on and let it sit for a few minutes (to finish the boot process) can you eventually use the volume up/down keys and hear the usual clicks/pops that occur when you press them?
Hopefully that helps!