Yea, you would get beeps if the CPU were bad. Did it beep at all when it was working properly? There should have been one beep at post telling you all is well.
If you have multiple sticks of memory try one at a time.
You could download Memtest86+ that will test the memory. There are versions for both a bootable floppy or CD.
If you have a spare PSU, try that if the memory works out.
You could remove the motherboard, and set it up on the antistatic bag it came in and try booting it from there. That will eliminate any shorting issues.
I'll try my other computers psu, i have no onboard gpu. The thing thst bugs me is, that it was working fine last night, i shut it down, woke up today and it wasn't working