Stranded on a road trip, '90 ZR-1, no crank

[ZBrink]

I got stranded at a gas station 2k from home in northern Arizona. Just bought this '90 on Friday. Have started it 15+ times no issues. Got back in it after filling up with fuel and the starter isn't making any cranking sound. I enlisted some strangers to try to help me push start it, not sure if I did it right, but it didn't start that way either.

Anyone good at troubleshooting something like this?

Zack: 217-725-7760 Feel free to call if you're good at this and willing! I'm alone, 2k miles from home, currently in Flagstaff.

EDIT 1) It has battery power, the headlights, HVAC control and radio all power on. When I turn the key to On, I hear a humming so I assume that's the fuel pump working? Not sure if relevant but the cluster itself does nothing when I turn the key to On.

EDIT 2) I was able to push start it in 2nd with some kind strangers help. Engine would seemingly and randomly die which make me think fuel as well. But, why no crank if it's a fuel issue? Was able to drive it 60 miles to a hotel. It cutout once at highway speed, I shifted into a lower gear and it fired right back up, at speed. Not sure if relevant/related, the gauge cluster goes out when the engine dies but the rest of the dash has full power. The no crank is my biggest worry in getting it home as I won't always have people able and willing to help me push start.

EDIT 3) Anyone know how to bypass VATS on the fly with generic parts I can get at an auto parts or hardware store on a Sunday? I was going to try and get some wire and clips to bypass the clutch switch as well. The Security light is flashing but maybe it stays solid or comes on when the engine cuts out and I'm just seeing it happen in that split second?

EDIT 4) It started right up late this morning but it has cut out on me twice while driving at highway speed and both times I was able to get it running again while still at speed. Is this related to my no crank issue or a separate issue?

EDIT 5) I want to give a shout out to the two Daves and Mike for calling and advising me over the phone with their time and expertise. So much appreciated! The issue has not be diagnosed or solved as of yet but the car has been starting and I'm still pressing east, in Oklahoma City for the night. The car is going to need numerous repairs/maintenance items tackled but this is definitely at the top of the list.