My aunt's 2001 sebring convertible wont start on its own. I can jump start it, but even after continuous running for 20 min. plus it will not start on its own. The battery checks out as fully charged.

 

Have you removed your battery connections and cleaned them? I assume you are boosting up top. I've had a couple of cars corrode between the battery side connections and cables. They get a black film that give poor connection, so they won't crank the engine. Won't hurt to look.
Charlie