[wiswind]

I would try the battery.

One of my co-workers just went through a similar issue.....
He had a place to a "in car check" and they told him that it was the alternator. I had loaned him my charger and told him to charge the battery before starting the car with the new alternator.....
They jump started the car....and it ran fine.....re-started.
Then later he went out.....and the car would not start.....he put my charger on the battery....and it blew the charger.
They got a bigger charger.....and it tripped the circuit breaker on it.
He bought a new battery.....and when he removed the plastic cover off the old battery......they could see that it was bloated.....
New battery solved the problem.

It sounds like your battery is not as bad as his was.....I had never heard of one like his...... But your problem sounds just like a bad cell in the battery.