First, check cable connections at the back of computer. Also, the monitor may have a cable connection so check the back of the monitor too.
Second, if you physically moved the computer, you may need to take it apart and ensure that the cards are seated properly. Take that opportunity to clean all the dust out. Take the computer outside, take the side of the case off, and use compressed air to blow all the dust out. Your wife/kids/sinuses will appreciate you doing this outside.
If it still doesn't work, uninstall/reinstall video drivers.
If it's still toast, check for loose heatsinks, fans that don't rotate, loose power connectors, etc.