Battery replacement is fairly simple if you have a basic knowledge of electronics repair. I've done it a few times, and need to do it again on my spare key now actually. If you don't have experience, then as upallnight so "eloquently" put it... just go order a new key and send your current one off for repair.
Part number for the battery is: Panasonic VL2020
Edit: And if you aren't comfortable dealing with the above batteries incorrect pin placement. This one has the correct 90 degree pin placement for the diamond style key circuit boards.
https://www.amazon.com/HQRP-Battery-...mw+key+battery