is it possible that your blazer has a remote start from factory or aftermarket? even if it doesnt have the remote someone at one time may have installed one. i am assuming this truck is new to you and this was an existing problem when you bought the truck or shortly after you got it home. even though you already replaced the ignition switch it could still be a bad one. another member with a similar problem was pointed here
this sounds to me like a wire somewhere in the starting system is shorting but that could be anywhere between the initial switch and the starter. even a unknown of remote start wire shorting. it could also be a problem with the charging system check your grounds and have autozone or the likes test the battery. and check the output on the alternator. i once had the dc rectifier go bad and my car did all kinds or weird **** and eventually the battery completely died and the car wouldnt do anything even a new battery didnt fix it. swapped alternators and it was fine.
might also just play with things on the truck and see if you can affect the problem by doing things like messing with the radio, heat/ac controls, lights, multi-function lever, ect. if any of them affect it youll know what is shorting to what.