if you can get the stereo out of the dash make sure there’s no obvious signs of damage to any wires and that all the looms are securely put together and nothing is loose in any sockets or clips. if its an aftermarket stereo that has one of those loom adaptors there not usually very good at a tight connection at the blocks so I would check them. if all is okay with everything back there and your having problems with more than one function on the radio I would check for any water damage or internal damage to and boards. if all your cars other electrics are fine then changing the battery wouldn’t fix anything unless the new battery is having voltage problems in which case all your electrics would be going strange. if its an aftermarket stereo and you have the original or another change them around and see if you still have the issue . if its a standard stereo it might be worth seeing how much one is to replace on the internet second hand, pretty easy to do with YouTube tutorials and usually cheap enough to do rather than paying for electrical repairs. hope it was of some help to you