I presume it is a Desktop (if not then let us know if Laptop/Notebook)
For testing purposes, disconnect the harddrive and any devices attached via usb (printer etc) now switch it on and see if the BIOS screen come up. It should get to the stage where it tells you 'No bootable device found' (when you want to switch off hold in the Power button for about 10 seconds and it will power down)
Let us know if you get it to that stage and leave it on for about 10 mins to make sure it is stable.
Whilst side is off pc and you are testing look to make sure all fans are working.
This will eliminate any problems with the harddrive and Vista install.
If pc still switches itself off, then try reseating the ram memory sticks, they may have worked loose, as could any other bits and cables so that is next thing to check. While you are in there, clean out any fluff and dust.
Safety note: DO NOT touch anything or try to clean while there is power to pc, unplug at mains socket first.