Obviously, you have removed the battery now, the other thing to try is to go into the menus and reset the camera.
While you can re-install the firmware, its via a trick, and probably not something I'd recommend to the average user.
If this is the original battery, consider that it might just be failing, so try a new battery or at least a different one that is not 6 years old. A battery is lucky to last more than 4-5 years.
You imply that removing the memory card causes the problem, but can you confirm that it does not have the issue with the card installed?
Its possible that you have a bent pin in the memory slot of the camera that is shorting out power, and it somehow is pushed away from the short when a CF card is installed. You need good eyes and a good light to view them, a magnifying glass and flashlight can help. It can be tough to see a bent pin.
My daughter has my old XTi, they were a good camera, and many do not know that they have a mechanical AFMA feature that lets you adjust the sub mirror position, and thus lengthen or shorten the AF path. This is useful if the focus on all your lenses is off a little. Canon stopped doing that after the XTi.