The first thing to check is to make sure the computer is getting power. If there are no lights and/or you hear no sound when you try to turn the computer on, firsty check the power cables on the back. If the computer has a 110V/220V switch on the back, make sure its set firmly into the 110V position. In some cases, the computer make be connected to a surge protector; if this is the case, make sure its turned on and it is receiving power from the outlet.
If there are no error messages pointing you to the problem, check to be sure that the printer is still connected, via USB or Ethernet cable or—if a wireless model—that the Wi-Fi is enabled and that you're connected to the right network. The printer driver and software needs to be installed on the computer you want to print from. It's possible that the driver has become corrupted; it should be reinstalled; check the manufacturer's download page for the latest version.