Suddenly my computer turns off, help - LONG post

VERY LONG POST!!!, very sorry for the length

i've tried out all the solutions you came up with but nothing different...

here's the problem again with MAX detail (may be a bit different from the first post)

problem 1. the one about the computer not turning on when i press the button seems to happen only in the morning the first time i try to start it up after i wake up. altough it is not as bad as before but still it takes about 5 mins to switch it on. It also only seems to happen when i pull the plug out, if the plug is still in then the computer will start up fine in the day but if you leave the plug intact and leave the computer off for the night the same problem occurs.
could it be because of static electricity?
could it be becuase the computer is too cool in the morning? (its about 22C in the morning here)

problem 2 - VERY annoying!
Although this is just a little thing i noticed but i think it has nothing to do with it, this problem only occurs after 11 am
when i use any graphics and CPU intense programs : physics modelling or playing games etc...the computer suddenly just switches off itself! (btw i run these programs: games and physics modelling etc.. for more than 4 hours continuously two times a day so 8 hours a day, i'm studying advance physics here) also once this happens once then after that the computer won't last 10 minute into running these CPU and GPU intense programs/games.
and sometimes after it switches of itself for a few seconds it will switch on again but then right after the beep after POST it switches off again and then a few seconds later it switches on again and this process will continue until i finally pull the plug out of the socket. but other times it just switches off and never comes on again! this is weird!!!
CPU temp is around 53-55 no more than 56 though and graphics GPU temp is around 50. so this is not an overheating problem for sure.
i scanned for viruses, so no virus too!
another instance that happened today was when i was watching a movie, i finished it, closed it walked away for a minute, came back, press a button on the keyboard and bang! the computer went off??????

and just a reminder, this only happens with graphics and CPU intense programs, i can defrag the whole night long and the computer won't turn off.

a something maybe you should now too, i cannot restart my computer, i issue a restart command, the computer shuts down normally but then the computer turns off and it never comes on again, i have to take out the plug and replug it to turn it on again. ?????
could it be:
motherboard broken?
CPU broken?
RAM broken?
keyboard shortcircuit? (weird guess considering the pressing button problem)
what else?

p.s. i've change vid card and PSU already so its not broken for sure

sorry for the length but i feel that if i do not get in depth with the problem it may never be sold and i may have wasted quite a large sum of money....