Sometimes power supplies do just die one day, not that uncommon really.
They almost always have a fuse, pull the P/S, cut through the sticker that says no user serviceable parts, open it up, and take a look.
If the fuse isn't blown, it could be dead, or the power isn't getting turned on through the motherboard, meaning it could be dead, or the switch could be bad (easy to test, just pull the power switch plug off the board and short those two pins for a moment with a screwdriver).
Typically a power supply can be had for $30ish.
Wait, a 5yo Gateway.... throw it out.
