My distributor, cap, rotor, wires, plugs and air hose were all stolen off my Toyota Camry. A "shade-tree" mechanic replaced all the parts except the hose, but the first time I drove it all the dash lights came on and it stalled. I tried to restart it about 5 times and it cranked but wouldn't turn over. It sat for 20 min waiting for him to show up and when he did it started right up. It didn't do it again for about 3 weeks, then it was daily for 3 days, then every time I drove it. The last time I repeated the process (try to start at least five times and sit for 20 min) it wouldn't start, and the second time I turned the key it made that grinding noise that a car makes when you try to start it and it's already on. I waited another 20 min, it started, I drove it home and parked it. A different person suggested that it might be the fuel pump so I replaced that. It idled for 1 1/2 hrs, then cut off as soon as I put it in drive and made the grinding sound after I tried to start it the third time.
You may be having two different problems. First the grinding noise may be standard bad starter type stuff. second, did you say they stole parts or the whole car and you got it back with those items missing? I'm supprised about the air tube issue, If I remember right the toyotas are MAF (mass air flow) set ups and won't run without the intake tube between the sensor and the throttle body. It's quite simple "the computer cannot fuel it if it doesn't know it's eating". The starter issue seems to be possible weak solenoid or mechanical misalignment. hope not bad teeth in the flywheel. A little more info might help.
When engine failed to start, you need to find out what is missing. Guessing is costly and would not solve the problem if replace something that is good.