So I started my 95 explorer yesterday morning, went to work, did some
mid-day errands, after work went to store, came out of the store and
it wouldn't start, no power. So I'm thinking it's that dodgy battery
terminal (-) connection. I get something out of the back, tap it a
little bit and the power comes back. I try to start it, but when then
starter engages the power goes out again. I repeat this thing and it
happens again. Thinking the cable is bad, I get the jumpers and
connect the terminal to the power steering bracket in the hope of
getting a better ground connection. It doesn't help. A guy comes to
help and gives me a jump. It starts with the jump, but when we
disconnect the jumpers it dies, the whole system goes down. A tap on
the terminal powers up the car again but still no start. The battery
is a few weeks old and seems to be fully charged. The alternator was
replaced last year. Anybody have any ideas what to do? I'm thinking
that this could just be the battery cable, but once the car is started
shouldn't it keep going even if the battery is disconnected?

Any help will be appreciated.