|Just some general things to check:|
Did anything happen to it between the last time it worked OK and the first time it didn't?
The fact that LEDs flash and fans and driives spin only means the power supply is putting out 5 and 12 volts. Since the power supply must provide other voltages at suficient current we don't even know if it's good.
If the power supply has a 115/230 voltage switch, make sure it's in the correct position. DON'T GUESS and only switch it with the AC cord removed.
With the AC cord removed, open the case and remove and reinsert the 20-pin (or 24, whichever you have) main power supply connector to the motherboard. Do the same for the 4-pin atx connector--the one with 2 yellow and 2 black wires. That way you'll be sure they're making good connections. Then plug the cord back in and start it up.
If that's not it then remove the AC cord again and temporarily remove all the cards except video and disconnect the drives. Plug the cord back in and start it up. If it works then one of the disconnected items must be at fault.
If that's not it, it's probably either the PSU, motherboard or both. If possible swap in a known-working compatible power supply. If that's not it it's probably the motherboard.
The mantra of the aging hippie--"Power to the government, right on"