When you power up the computer, do any of the lights on the drive itself
come on? If not, the power wire may have come off, and easy fix (4 wires,
plugs in back of drive). There are usually extra power connectors, if so
try a different one if it's connected and still doesn't work. The IDE cable
may also have come off, or if it's a newer unit, it could be a serial ATA
connection, which is notorious for coming off. Most likely though, the
drive would open if those wires were off, but not if the power wire was
disconnected or not plugged in fully.
If it gets to where you can see the drive in My Computer etc., and it still
won't open with the button, try right clicking the drive and choose 'eject'.
Don't use the suggested screwdriver...there should be a tiny hole below the
drawer, and a firm steady push with a straightened paper clip will almost
always open them, and not cause damage to the drive. Push it straight in,
then when it hits the latch, press firmly and it should open.
Gary