Sucks all electrical when try to turn over.

Recently on my live-aboard 1981 28 Sabre with 13HP Volvo Penta, when I try to crank it up all I get is a fraction of a second of starter action then a dead electrical.. when releasing the key, I have power, but substantially weaker until charger kicks in... I feel that when charger isn't charging I may be getting a discharge, but I can't fathom where. Lights often dim when bilge pump comes on... There seems to be a lot of places to look, so can anyone point me in the most likely direction, or has anyone actually experienced this and solved it..?

Check the fluid level in the battery and the be sure the battery connections are clean and tight. If you think the battery is draining, charge it and disconnect it to see if if is holding a charge. Might not be the answer, but it is a start.

How old are the batteries?