Push, jiggle, jab (whatever) the on/off switch. Sometimes they get dirty or just plain old.
Check to see if it is plugged in - at the wall, the surge protector (if you have one) and the back of the computer.
Plug something else in the wall outlet to see if there is power there.
Check the plugs to see if they are bent - not making good contact in the sockets.
Listen to the computer. It might be on and the trouble is with the monitor.
If the computer is on but the screen is blank, check to see if the monitor is turned on - all plugs are securely plugged in. If all is on, check the settings on the monitor - contrast, brightness
PRINTER WON'T PRINT
Is it turned on? If so, turn it off then back on.
Checked all AC plugs from the wall to the printer and anything in between.
Check the cord from the computer to the printer. Jiggle the connectors gently to see if they are firmly seated.
Is there paper in the printer? If so, is it feeding properly?
Is there any paper jammed in the printer?
Are the ink cartridges empty?
Turn the printer off and shut down the computer. Re-boot and turn the printer on. Try the printer again. Click "Start" - "Settings" - "Printers". Click on your printer and make sure that it is the Default Printer. (XP - Click "Start" - "Control Panel" - "Printers and Faxes")
In Printer Settings, make sure that there is not already a printing job in progress that shows an error.