At the internal side of the switch there are 2 cables that are solded to the expansion card (they are OK) and 3 cables that go towards the Amiga mainboard (2 of them are desolded from the switch)
Sounds like someone's done the 1MB chip RAM hack, and made it switchable. If those wires have come off the switch lugs, you'll have a very confused Amiga! Even with them on and working, you would need the expansion ram to be working with the switch in one position, but possibly would work without it when the switch is in the other position. (How many positions does teh switch have?) Can you possibly attach some digital photos of your Amiga board, especially where the wires attach to the motherboard?
First order of business is to find the 1MB Chip RAM hack and verify that the wires to the mainboard are in the same locations.
Is it easy to get and replace that battery or maybe I should look for a new expansion card?
If the battery has damaged the card, you may not get it working by removing or replacing it. If actual data bus tracks are damaged, you will need to get another expansion card. These are plentiful as almost everyone had them.
