I have a 2009 Chevy HHR it was working fine I left my lights on and the battery went dead I jumped the car off from under the hood. I then let it sit for twenty minutes to charge battery up.. after twenty minutes I cut car off then crying car up again the car worked fine.. the next morning I go in to crank car and nothing happens the lights and traffic everything comes in but car does not turn on.. I take battery out and have it checked it was good I look under hood at fuse box and the number 5 fuse (starter system) was blown. I replaced it and when I put my key in ignition and turned car still didn't crank and fuse was blown again how do I fix this problem?

 

Welcome to the site, seems like you might have a problem with the cable from the post on the fuse block under the hood to the starter either touching ground somewhere, or the starter itself could have given up.
I suggest disconnecting the battery, negative cable in the spare tire we’ll.
Then test continuity from the starter cable to ground.

The larger red covered terminal on the lower left of this fuse block picture