Welcome to the place!
I bought one of those things when they came out and liked it a lot. The battery will be inside and probably circuit board mounted. It should be replaced ASAP, if it hasn't been. That unit is probably around 30 years old. Hopefully the battery hasn't corroded and started to eat away at anything. I also remember mine running quite hot. I wouldn't be surprised if there are bad caps considering age and heat trapped inside the thing. Start with the battery and see how it works after that. If you still have problems, I'd probably next check or replace any electrolytic caps in high heat areas like next to voltage regulators, etc.