HELP Cobalt Will not start

I have a 2006 Chevy Cobalt and when made a stop at a store and when I came out the car would not start. I'm not even getting any click when trying to start it but I do have lights and my dash lights up. I tried to get a jumpstart but it did not work so I had to get it towed home. I have been having an issue with the HVAC control fuse blowing out. I was also about to take it in for the recall issue with the gas tank. If anyone has any suggestions I can true I would really appreciate it. The tow truck drive thinks it may have to do with the computer.

Sounds like the theft kicked in, these cars are bad for ignition switches, it thinks that the cars ignition is being tampered with and wont start for 10 min.