I had the same issues within the last month. I contacted customer service and told them the issue. They sent a refurbished unit as a replacement. They give you two options -- you can either send your defective one in first, then they send you the replacement, or you can pay ~$200 up front and they send the unit immediately and refund you after returning the defective one. I was pretty impressed with how quickly they responded and got me back up and running.
Same experience as OP, stopped using my 130 for awhile when I got my 530, went to charge it up but wouldn't charge or turn on unless plugged in. Garmin support quickly exchanged my almost 3yr old unit (very few questions asked,) for a refurb which I just received. On one hand, stellar customer service from Garmin on an out of warranty product but still concerning on the design/failure front for those affected. Not sure why this happened, but I plan on keeping my130 battery charged during long periods of disuse may help?
All of these things are bad for lithium batteries:
Lithium batteries will remain usable the longest if they live in the 40% to 80% charged range. For long term storage I would charge to about 60% and check charge level two or three times throughout the year and keep it centered at around 50% charge.
Thanks! will keep this tips in mind for my devices.