does the whole machine power down during start up or does the monitor just switch to standby?
if its the monitor check all leads are connected firmly,try also removing any tv out svideo leads and just leave the monitor connected to try.
if its the whole machine powering down at start up then my guess is it could be the power supply.
crashes, freezes in windows etc can be caused by this but first check you have the latest drivers for motherboard graphics sound and patch any games also.also make sure windows is up to date too click here
have a look in control panel/administrative tools/event viewer for any errors listed at the times you may have had a crash for more info.