Dr.Toetags

Just had a new battery installed and that did not fix my issue. I am at a loss here on what the issue is...

I have a 18' Sierra 1500 and randomly in the middle of the day it decided to not shut off the motor. When I turn the key back all the interior electrics go off except the motor and blower (as if I auto started the truck). I have searched the Internet thoroughly and it seems this is a hard issue to find a definite solution to. If anyone has any information to point me in the right direction would be greatly appreciated. I am also throwing 3 random codes with a check engine light, P0700, P1682, and P0561. ANYTHING AT THIS POINT WOULD HELP!!!!!