Morris Plains, NJ
Exact same problem here. I got my power back today, and had TV and internet for about 3 hours before the battery ran dry. The BBU is just not powering the ONT.
Even though I explained that the ONT was OFF, tech support ran a "line check" and they said that there was a "fiber break" and they would send a tech on Monday (sigh).
I took out the battery, found a spare 12V 2A PSU, jury-rigged it to the terminals where the battery plugs in, and hit the battery backup button. Everything's back up and running - I assume the ONT will just see a magical "backup battery" with infinite juice...