No power to fuel pump relay?

Thank you! Okay, so, I did what you said and found blown fuse replaced it. Got power back to fuel pump relay, I jumped it correctly with in fuse wire this time (should of the first time lol) pump turns on and stays running. Tried to start it while bypassing relay but still just shuts off right after startup. To me sounds like it's the stupid pass lock system. Because with everything else working fine it must be shutting off injectors due to the pass lock, right? I haven't tested the power to the injectors yet but even if one or more was not working the van wouldn't just shut off it would run badly, right? I don't want to have to text info if not necessary, it looks like there kind of hard to reach and probe. I have tried the pass lock relearn but maybe I missed something? Any ideas?

Also, when trying to do the reset my security light comes on the first turning to on position then goes out a second or so later, then comes back on and stays on. No matter how long the light doesn't go out. In the reset it says it will blink stay on then go out after ten minutes and then turn the key to off position 10sec back to on until light goes out again reapt. Etc. But mine just stays on. I even left it on for over an hour because I heard will reboot or Sumin after left in position for hour. Supper frustrating, I've been without a vehicle for over 6 months. My buddy's mom lends me this extra van she has. We drove it up to Washington from OR. No problems, gas gauge doesn't work so you just have to estimate mileage. I fig it was getting low since the last fill up but was super tired, so I parked it at home instead of getting gas that night. The next day came out and the battery was drained because the stereo got left on, I think. And it's done this no running thing since then. I went and put like 4 more gallons in tank just to make sure wasn't out and still just does the start and shut off. Just some more info on the back story. If it helps at all, lol. I originally thought the security got tripped cause of the drained battery maybe, but this is my first GMC and pass lock nightmare, lol.