a 12V battery should read over 12V, about 13.8 static and as much as 14.4 when running .... I'd first check all cable connections for cleanliness and tightness if that was the last thing touched - next take it to an auto elec shop to check alt output under different conditions [could be the regulation circuit] and get the battery load tested as well - if it holds a charge for a short time but not overnight it could be a bad cell or other battery internal problem - defective batteries do happen
Bill
