|Disconnect everything from the motherboard except the case wires. Remove the RAM, graphics card and any other cards.|
Turn it on, and you should get error beeps for the missing RAM. If you don't, the problem has been narrowed down to the power supply or motherboard. Most likely the power supply. They fail more often than motherboards.
Don't be misled by the fact that you see some signs of power. The power supply has to supply several voltages, and just one missing or out of tolerance can cause your problem.