the motherboard led is on, i really don't know what to think
Without knowing what LED is lit, or what it is doing, that really means nothing other than the motherboard is getting
some power.
As Last_Troll noted, a lit LED could indicate a number of things.
Remember, your PSU must output 3 different voltages, +12VDC, +5VDC and +3.3VDC. The most basic lit LED indicates the PSU is, at least (perhaps only) providing the required +5Vsb standby voltage. It does not indicate all 3 voltages are present, clean, or stable.
Since EVERYTHING inside your computer case depends on good, clean, stable power, the first thing to do is to swap in a known good PSU to see if the problem persists.
Unless the computer recently moved and knocked about a little, I personally don't see how this could be due to you replacing your CPU heatsink since it worked fine after that for a whole month. IMO, if you did it incorrectly, problems would have surfaced immediately, or at least after just a few power (heat-up/cool-down) cycles.
That said, you did thoroughly remove the old TIM (thermal interface material) and clean the mating surfaces before properly applying a fresh, new, thin as possible, but thorough layer of new TIM, right?
BTW, why did you replace the old cooler?
If the second power supply does not fix the problem, then I agree, you are going to have to do some trial and error checking. Just remember to unplug from the wall first (to remove all voltages - including the +5Vsb voltage) and remember to touch bare metal of the case interior BEFORE reaching in to discharge any static in your body.
