van died while idling, dead battery, changed it, now won't start

Hi, I'm a Mom with only a little knowledge about vehicles, but I can follow directions if I want and I'm really hoping for some help. I've been reading up trying to figure out what is wrong with my beloved 180K miles "Mom of 4 Taxi" which is a 2006 Chrysler T and C. I have little money for towing/repairs so I am trying to do this myself.
In short, my van, which had been running great, died while idling when I got out to get one of my kids. Battery was dead, no lights etc. I used my battery jumper, it started right up and I drove a mile or so before it died again at a stoplight. I got it off the road and decided to walk to get a new battery. Replaced the battery but noticed one cable was so badly corroded that it almost split apart. It started right away and I drove it home after getting more gas {said I had 11 miles to go yet} but after, at one point, it almost sounded like it was going to die but didn't. Next morning it started and ran great during drop offs to school, about 20 miles.
That afternoon it started right up but died before I could back out of driveway. It has not started since. Multiple tries. I replaced the cables to the battery thinking corrosion and nearly broken terminal piece was the problem. It cranks but wont turn over, and would start with starter fluid momentarily. I think fuses are ok, read something about relays and switches, anti-theft auto gas turn off, and keeping hope that it isn't the fuel pump which I now know is in the gas tank and way beyond what I could do. Anyone kindly have any thoughts on what I could do next? Should I try replacing the air filter? I sure would appreciate any other advice or thoughts.
One other thing is that door locks and windows only work when they want, but doubt its related. Thank you for your time.

I just figured out how to check for codes and after turning key three times it said "done" with no codes displayed. Now what?

Starts and stops on starting fluid is your big hint- a fuel delivery problem exists.

Time for a fuel pressure check- Autozone will lend you the kit.

Fuel pump needs good voltage to run right- check connections, relay, fuses etc.

I have beat my fists on fuel tank while someone tries to start it and activated the stuck fuel pump before- further proof a new FP is needed.

Ya, agreed with brcidd. The starting fluid takes the place of fuel. The fact it started momentarily says it's getting spark. Just want to add your van has no fuel filter. Just a screen on the pump inlet in the fuel tank. The fact you're not seeing codes is another indicator you may have a pump problem. There's no code for the pump. Odds are the pump failed but someone will have to verify it's getting power before changing it.