Since you weren't having problems previous to this, I'd suspect the battery first. Second choice would be a short, but my bet would be on the battery. Is there any way the jack is shorting against a wire or the shielding?
It's totally possible to get two questionable batteries in a row, I've seen way stranger things happen with 'new' stuff. I worked in a truck shop once where we put 4 new blowers in a truck and every one of them was bad... of course the guy thought it was our fault, but it was a bad batch at the factory and we just happened to keep getting the 'right' ones... Batteries are also age sensitive, if they sit in the store, or in a drawer, too long they won't be up to par. Measuring them without a load really doesn't tell you enough about their health.
That said, that's why I like to put the bypass switch in my electronics, pull it up and keep on playing "o) Everything breaks eventually.