|"Would a Compaq - Desktop - 4GB Memory - 750GB Hard Drive|
be good to be used for gaming?"
What about the rest of the specs? Most important are the CPU & graphics. Onboard video is generally not good for gaming. You may be able to get away with using it for older games, but if you decide you want to play newer games, you'll need to upgrade to a gaming video card & may need to upgrade the power supply too.
If you don't know all the specs to the computer you're considering, post the model & model number. HP/Compaq made a LOT of different computers.