As the seller had described, there was corrosion in the battery cap and the screw to keep the cap in place had its threads worn off (so you pretty much had to HOLD the cap in yourself). As a temporary solution he placed some folded foil in there to act as the contacts.
Here's the corrosion on the cap, and the bit of foil.

I put in some fresh batters, did a battery check, and it ran just fine. However, when I tried it again, the motor wouldn't run anymore! Checked the batteries, and the meter now indicates there's insufficient power.
Only the cap appears to have any corrosion. Inside the battery compartment there isn't any.
What can I use to clean up the contacts, and what should I do to ensure that cleaning them won't screw something else up?
Also, the manual zoom ring is just not smooth. How would I fix this?
I want to try this before I look around for a repair place.