Battery or something else: the quick sort
A cell fades rather than failing in one step. Range that shrinks over weeks, a button that wants a second press, and a low-battery warning in the instrument cluster all point to it. A fob that died the day it went in a pool, one button that quits while its neighbors work, or buttons still dead after a new cell point somewhere else.
Reading the number on the cell
Coin cells are named by size. In CR2032, the 20 is the diameter in millimeters and the 32 is the thickness in tenths of a millimeter, so a CR2016 is the same width at half the thickness. Buy the size marked on the cell you took out, not whichever one drops into the slot, because a thinner cell can rattle loose and lose contact when the fob is bumped.
When a fresh cell changes nothing
Then the pairing or the fob is at fault. A fob whose rolling code slipped out of step can sometimes be brought back with the resync steps in your manual. One the car no longer lists needs fob programming: $79 to $119 with us, $120 to $200 from a dealer.
A snapped battery clip, a cracked solder joint at the cell holder, or green corrosion after a wash means the board is finished. That calls for a new key: a remote head key from $165, or a push-to-start smart key from $229.