Car will only start with a boost

I have a 2002 Jeep Grand Cherokee v6 automotic. Car would not start, tried boost, worked, but when I put it in reverse it stopped.  Battery charge checked out ok. Boosted again to start and ran for 1/2 hour. When I turn it off it will not start again without a boost.  Cleaned battery terminals, still same probelm. Any idea? bad starter?