Sounds very much like the battery is dead or has shorted cells. You could have it tested. A 12 volt battery that reads 12.5 volts is nearly dead. A good battery that has been kept charged properly should read over 13 volts in storage mode or when disconnected from shore power, on shore power it should read around 13.6 volts. With engine running, and charging via the engine's alternator it should read around 14 volts. Cleaning connectors at battery of corrosion and keeping electrolyte levels above the plates with distilled water helps prolong useful life of batteries.