@OP
I hope you haven't dumped your batteries yet. Main reason, it's hard to imagine both batteries died the same day. Just do what you would do in your wife's car in winter and a failed cold start.
- take both batteries home, for some TLC
- wait until they warm up in your garage, then "slowly" charge (0.5 AMps over night ?), any observations ?
- measure and note voltage after full charge and again 4 hours later,
- if your electronic charger doesn't seem to work, the battery's voltage may be too low, for the measurement circuit, try a constant voltage charger for the first hour, easy does it,
- if the battery seems ok, put her back into the plane, turn on a few lights and a radio, and draw 1.5 A max.
- wait and see what happens, turn everything off, wait a few hours (or longer) and try again,
- is she holding charge, has the voltage dropped, etc.
- use these data for guided troubleshooting (you'll find the flow charts on the internet).
- repeat with 2nd battery
This won't bring a dead battery back to life, but you wanna double check before you dump 750$, no ?