Start by removing BOTH the battery cables and cleaning the terminals on the battery and the cable ends themselves. Then make sure they go back on nice and tight. These cars are sensitive to dirty/corroded cables and can cause all kind of strange things like this.
Also check the grounds at the transmission bolt. It's on the right side (if you are facing the motor from the front end) near the starter. Should have 3 wires bolted to the stud on the transmission. Might try giving those a clean/check as well.
