Is it possible for a battery to be so bad that can't even jump start????

yep. charge the battery and have it load tested.

A dead shorted battery will not jump start .If attempting to charge, do it on slow charge rate

When a battery starts losing power and goes bad, it's usually because the cells get sulfated. It makes it harder for the electrons to pass between plates to make and hold electricity. Simply charging a battery won't get the caked sufate off lead plates. Desulfators are used to knock the suflate off, but they take time. I have a couple of batteries I brought back from the dead, but they're simply for emergencies. A new battery would be a wise choice. IMHO