Will not start

This truck was my Dad's baby. He passed away last August, and I have been trying to get things up and running. The battery that was in it wasn't charging or holding a charge, so I replaced it. When we put in the new 12V battery, the alarm went off. We got that stopped with the fob. Then we started the engine and it stayed on for a few seconds and stopped. That happened a second time. Now, it won't start but it is trying really hard to turn over. So, things we have ruled out: No codes, not the starter because it's not clicking, fuel injection seems fine because we are smelling exhaust and it's trying to turn over. I have a charge box and could try jumping it, but I think I shouldn't have to do that since it's a new battery. Checked for corrosion haven't seen anything alarming because everything under the hood is in excellent condition because my Dad was so meticulous. We are concerned that the gas may have separated since the last time we were able to get it started and running was in February.

We are at a complete loss. Any advice is welcomed!

Thank you! :D