Car not starting

The other day while driving my car around the block, I stopped at a stop sign. As it shifted back down to idle it began to sputter out and eventually shut off. I cranked it a bunch and eventually got it restarted by pumping the gas pedal. Got it back home, parked, and it continued to run just fine for the time being. Turned it off and back on a few times and it started after some effort each time. I noticed that when gradually applying gas smoothly, it would accelerate smoothly, but if I gave it a lot of gas quickly it would begin sputtering rough until RPMs were pretty high then it would run smoothly again. I left it for the time being and went to bed.

On waking up the next day, I discovered it would no longer even start. Had a buddy look at it, he suggested the fuel pump should be priming and that it was not. Started troubleshooting at this point.

Checked the relays by swapping them out with known working relays, they all seem to be good. Checked fuses, fuses seem good as well including the fuses in the kick panel. Jumped the FP and B+ ports in the diagnostic jumper array and the pump engages just fine when I turn the key on. On removing the jumper, it does not prime or engage. I read someone on a Toyota forum suggest that some Toyotas don't engage the pump to prime when the key is turned over, but I don't know if this is true or not.

I tried starting the car with the pump engaged just to see if I could get it to start even for a second with the pump manually switched on, but it would not start. Tested farthest spark plug wire from the distributor for spark using a spare plug, and it is getting spark. I haven't checked the others yet.

Checked for trouble codes by manually jumping the Te1 and E1 in the diagnostic panel, no codes. I haven't used a reader yet but will tomorrow.

Checked the belts I could see but they all appear to be in good condition, I'll look at them further tomorrow. I can't get to the timing belt right now so I guess it could be the timing belt but I'm not sure if there's an easy way to check it.

Measured the fuel injector resistance and it's reading 13.6-13.8 ohm, which appears to be within range for these cars.

Also note that we attempted to start it with ether to no avail as a last resort. It did not start, even for a fraction of a second. Just turned over and over.

Any ideas?

Happy new year!