Hello, I haven't had my 2003 4.3 Blazer long but I recently replaced the starter because I would try to start it and it would not turn over but if I waited a while it would start right up. I thought the solenoid was bad. Now, however since I replaced the starter, when I turn the key the dash lights up as it should but the starter NEVER engages. So, I turned the key on and put a screwdriver between the solenoid terminal and the truck starts right up. Also, I tried swapping the 3604 relay out even though I did hear it click making contact just to test it. It still won't turn over. Could it be the wire from the ignition side of the solenoid to the relay that is bad?

 

It could be the ignition switch, but (yes I know you replaced the starter, and assuming solenoid) the solenoid. My 96 lumina does this on occasion, I've replaced the ignition switch before this issue, and yes key on, screwdriver across the solenoid (only intermittently) have to do that to get it to start. I carry a screwdriver with me in the car.

 

Put a meter or light on the terminal on the starter and see if you get 12 volts when key is turned to start.

 

Since you've only driven the car 4 hours with a new battery, the most likely thing would probably been a loose wire on the battery. Check the big wires and the small ones both

 

Have you tried replacing the crank/start relay in the fuse block ? You could have a bad set of contacts in it that will Intermittently work and Not work .
Just something far less expensive than a starter and solenoid to try .