Q: Car turning over but not cranking?

I just got this car and the gas hand didn't work when I got it. Not that big of a deal. Well I drove this car from NC to South Florida and it did great there but on the way back in SC I ran out of gas. I added more gas and it cranked right up and I drove home, no issue. The next day it cranked right up and I drove to town. While in town it wouldn't crank. My dad came and checked it and said it's a fuel problem somewhere. He said it's like the injectors aren't firing. He said possibly a crankshaft position sensor. We left it a couple of hours and came back and he removed the air intake hose (maybe, I don't know much about cars) but his hand over it and I cranked it and it stayed on. No problems since then. We have driven it several times no problem. This morning my husband left the lights on and killed the battery. My dad jumped us off but it started doing the same thing again. It will act like it will crank, but then will immediately cut off, like someone cut the switch. Any ideas?

My car has 133000 miles.
My car has an automatic transmission.