Hawisia

Hi! Having some problems with our boat electrics. Currently moored in a marina and plugged into shore power however still having power issues. Red light which indicates low power on the inverter comes on frequently. Also noticed today that the pump to pump hot water from log burner heated water to the radiators, controlled by a thermostat seems to be struggling and I'm assuming it's a power issue. But if I'm plugged into shore power why should any of this be happening? Also have a battery charger which indicates that it's on 'float'.....whatever that means. Currently have a bank of 4 domestic batteries.....completely clueless, can anyone help?... Thanks in advance