Your fuel pump is likely working too hard and drawing too much current. If you get the car running for any length of time you'll probably notice that the pump case gets very hot to the touch. The pump itself is probably worn out. This can simply be old age, but it could also be precipitated by some other fuel delivery problem like a dead in-tank fuel pump (pre-pump), a partially clogged fuel filter, a clogged in-tank pick-up screen, or a pinched gas line (in that order of likelihood).