The buttons on the back panel don't work

On my 350D, a lot of the buttons on the back panel don’t work. The only buttons that do work are the left (metering), right (AF) and the backlight button. In addition, the information screen also doesn’t work properly. This is regardless of the mode the camera is in. This makes it impossible to change any settings for the camera.

I have tried to remove/replace the battery. In doing so I also reset the camera, and now I can’t set the date. Now the camera doesn’t let me take any photos, since the date hasn’t been set. Is it possible to fix the camera?