Have you tried to turn it on directly through the power switch pin terminal from the motherboard?

Meanwhile, look for the diagnostic lights found at the back of the cpu case. Observe them.

Then, pull the video card and a memory stick out of the motherboard and seat them again in their slots....

I think you have accidentally touched or moved the old stick. Pull it out and put it back. Maybe it was not properly seated in the slot.

What does "sometimes it doesn't boot" mean? Does your computer boot into bios or not or is it totally blackout?

Have you already tried powering it up by bypassing your front panel power switch...

I think he has used an integrated/onboard video.

See to it all the connections inside the cpu are tight and snugly connected.

No beep code sounds means no case speaker was connected in your...

A computer that shuts off at random times is often a heat related issue.

Check carefully your cpu fan again. Add another case fan to dissipate some heat inside the unit.

If it doesn't help,...

I think you've set your system in hibernation mode. Run your computer. Try to press your power button for about 10 sec. in order to discharge everything in your system. Or your bios settings has been...

Why don't you try to remove and reassemble the motherboard and all the components again. Maybe there is a faulty connection or short between the motherboard and the case.