This was originally posted on APC forums on 1/4/2016
It is possible that your BE650G1 UPS has suffered a failure. The user's manual would seem to indicate that a bad (or discharged) battery can be indicated by either the "replace battery" light blinking or both of the power and replace battery lamps blinking. Do you have the serial number for your UPS and the new battery?
Although these units are not terribly intelligent, the microcontroller inside may have become confused in some way. First, turn the UPS off. Then disconnect everything that is plugged into it. Next, unplug it from the wall and disconnect the battery. Finally, press and hold the power button.
Reconnect the battery and plug the unit back into AC power. Leave it turned off and let it rest for about eight hours. Then connect something like a lamp as a test load, and turn it back on. See what it does. If it works, try putting it back into normal service.
If you have a multimeter, you could check to see what the battery voltage is. A fully charged battery should read around 13 volts DC or so. Likewise, you could check to see if the charging circuit is working. Unplug the unit, disconnect anything plugged into it, and disconnect the battery. Then press the power button to discharge the unit, and connect the meter leads to the battery leads inside the UPS instead of attaching the battery. Plug the unit back in to the wall outlet, and it should immediately output around 12-15 volts DC at the battery terminals as indicated by your multimeter.