There's no chance you'll find a free computer anywhere. Simple ones can be as cheap as $100, and older ones can be even less. I recommend a laptop if your main concern is price, as with a desktop you need to buy the mouse, keyboard, and monitor if they aren't included.
To get a free computer may not be easy if you don't live in the right state or meet specific qualifications. However, some organizations provide free computers to low income families and the elderly. Visit the link http://www.ehow.com/how_2085103_get-free-computer.html for more details.
About once a year CPA firms and law firms get new computers. They will often gladly erase the hard drive and donate them to those with a need. I would draft a letter stating your need and start sending it around and see if something materializes. Good luck!