The shelf life on an unused lithium coin cell (these batteries) is about ten years.
We got well over 3 years before the orginal batteries started getting weak, so if you have a "mainly unused" remote? I'd expect it to work perfectly well after 4-5 years of sitting on the shelf.
Still, the first test is to put in a new battery. About $6 for a two-pack at your local supermarket or drugstore, about $10 for 5 or 10 on Amazon, postpaid. Often the same brand and often just as fresh. Or five for a dollar at the dollar store, not so fresh but at that price who cares?<G>
DO clean the contacts and keep your fingers off them when you replace the battery, some fingerprint schmutz can be a problem as it ages and blocks the contacts.