Possible electrical problem

I have a '98 Wrangler Sport (manual). Tonight it wouldn't start and it seemed just like a dead battery problem. So I get a friend to help me jump it and it starts right up. I take my foot off the gas to unhook the cables and it dies. So we jump it again with the same results. It will run as long as I keep the gas slightly pressed. Yet if it dies it will only start with a jump. Any idea what could be wrong? Any help would be appreciated.

I would suspect a totally dead battery ( is it the original ? ) that will no longer hold a charge. If the battery checks ok ( have it tested ) than I would bet the alternator is shot. If it were me I would remove both, bring them to an auto parts place & have both tested at once.