07 Cobalt hard starting after getting fuel

My Cobalt is hard to start after I get fuel. It has also died when I take the fuel cap off (after leaving it running to prevent the hard starting). My check engine light is on and one of the codes was for a bad fuel cap. I replaced the fuel cap but still have the same problem. Also have codes for faulty Purge Canister Solenoid.

I would like to look into this further for you. In order to do more research, I will need the VIN for the vehicle as well as the current mileage. Please feel free to contact me either here on the thread or via private message. I look forward to hearing from you. Thank you in advance.

Tricia, GM Customer Service.