Yes the battery is soldered in. based on my limited experience,Since you say the machine was fine until you had the power outage and you have no code for a bad battery. It would seem to me that this in not the likely culprit. Certainly check the 2.4 voltage to see how close you are to that. Reminder, this is a recharge battery so let it have some power before you test it. As stated in above posts, the c-01 code is a communication error between the top and bottom box. The battery itself won’t stop them from communicating. Just for kicks, I removed my battery and got a code relating to the battery. But top and bottom box were still communicating. Do you have ac/dc test meter? Check the voltages on the top box power supply. Even though you say the power switch is lit and the bulbs do light under test mode,
To a degree that means nothing because the power supply puts out different voltages for different things. My bulbs lit, my power supply switch was lit, I had c-01 code. In the end, I replaced power supply and it solved my problem. Not saying it will fix you but power outages and sudden surges raise hell with power supplies. So test the voltages if you can.