General malfunction (Houston, we have a problem - arrrrrrgh!)

Sometimes all that's wrong is that one wire is broken, a printed circuit board is cracked, or the edge connector that joins two printed circuit boards is making poor contact. The edge connector is the easiest to fix: just undo it, clean the contacts, and reassemble. If you are good at miniature soldering, cracked boards and broken wires are easy to fix using standard techniques.

Battery leaked or corroded

If you're lucky, the damage is confined to the battery compartment and all you'll have to do is clean contacts. Use a liquid contact cleaner if possible, applying it with a cotton swab, foam pad, or eye dropper, and then wiping it off. Abrasive cleaning methods (wire brush, sandpaper, etc.) work, but the surface is likely to tarnish again soon. Do NOT let liquids or dust get into unknown parts of the camera.