I have a 20D and it's all froze up.

Since I am going to be guessing on some of this...let us try to see what can be done.
Seems you are saying that even though the camera is off, it can still take a picture. That has something to do with the switch system, it seems.
If the battery is removed then there should be no power left, except what is residual in the capacitors, this could allow you to use the camera for a few seconds or so. This is not normal usage, and is not the way it should be done.
Here is something to try. Go to the menus set all to factory or default settings as much as possible. Some cameras have a reset button on the surface, and most have a set to default setting in the menus internally. In any case set all to default, and then test the camera.

If the camera continues to have problems, you may want to consider calling Canon Repair Service. Call the 800 toll free number for service. Give them your camera model as well as the serial number on the bottom. Inquire about repair. If it can be repaired, the cost will be estimated when you send it to them(With Canon this is free)return is free if they fix it, if not you have to pay the return postage. If not, they will give an option to get a refurbished unit as explained below.
Canon has great service for repair and they also have a trade-in or trade-up service to get a refurbished camera. This is a great service which I have used when the camera I had sent in was too expensive to repair, I opted to buy one of the upgrades which was a refurbished unit which included everything with the camera which came with it when it was new.

Just to tell those who are reading this, not only does Canon have this service, so does Nikon with some differences.

One other option you may want to consider, as I have suggested numerous time on this site, is to sell it for parts , repair, or as is on a site such as Ebay. You will have some money to put toward another one.