If the charging circuit has fried, then complete battery replacement sounds like your only option. But if just the cells have expired, then it's usually fairly easy and cheap to replace them.
If it were my device, I would pull the battery carefully apart, replace the cells, and charge it up. For about $10 for two new cells it's an experiment that would be well worth it IMO. If it fails, you can then start sourcing a whole new battery.