Either way, garmin’s user manual(link) says it is not needed. See page 36, saying “Data Storage Life: Indefinite; no memory battery required”

I don’t think that they’re saying that the button cell is some sort of undying thing, but rather that your traces and such are being written to nonvolatile memory.

I assume that you already went looking for a replacement cell and couldn’t find one, else you’d have replaced it rather than resoldered the existing one.

Assuming that the button cell is actually the problem and that it’s rechargeable, it occurs to me that you might try pulling the cell off again and checking the recharging voltage across the connectors to try to get an idea of what type of cell it is, try getting a new cell with similar characteristics. Might kill the unit doing so if you get the voltage wrong, but if it’s not usable now and you’re confident that the battery is the issue…shrugs

To be honest, if I had the unit, I would probably pitch it rather than to invest time in fixing it. It looks like this is a fifteen-year-old unit, and my smartphone is probably a more-capable GPS unit running free software. The value of the time I’d spend on fixing it probably exceeds the value of the unit. There’s a reason that consumer electronics repair isn’t much of a business. If you’re viewing the repair as a hobby or something, though, fair enough.