It sounds like aweak alternator something is pullin to much so then ur alternator is being over drawn so it can't compensate for the lose of power. Thats why when u leave ur car running and then shut it off u can start it. Cuz what happens when ur drivin ur alternator is rechargin ur battery so then u can start it back up right away. It could also just be that something is stayin connected to the power supply ( the battery ) when ur car is off so when u want to start it back up u have trouble cuz there isn't enough power in the battery.
My advice is to take ur car down to Autozone.......... they have free alternator, battery, and starter testing............. FREE OF CHARGE........ so take advantage of it ........... they can find out what is causing ur starting problem.

Elaine