The UPS on power outage will drop power to devices plugged into it.
Have you ran a Test button to see if the UPS works / battery works and actually provides power? A component may have failed inside the UPS, the battery may be bad, or the wire connection may be poor. Did everything work, tested with no power, with the previous batteries?
The UPS does not power back on when power is restored.
That's normally a setting that's configured. Staying off is safer, in case the battery didn't get enough time to charge back up and power immediately goes out again.