Mate has a Suzuki, three years old. Two keys, one not normally used and kept in a drawer. Needed it recently, and the remote wouldn't work. Took it apart and it has a replaceable battery, which was flat. Perhaps something had pressed a button while it was in the drawer.
The battery is a CR 1820. Couldn't find one locally - Boots etc - nor on Ebay. Dealer wants 15 quid...
A CR 1620 is the same size physically but smaller capacity. Works just fine - although may not last as well. Under 4 quid in Halfords. About a quid each for a decent make on Ebay.