i have a 1988 4wd truck. it has the normal 22re with a k&n filtercharger and downey header coupled to the 5 speed.
when i go to start it, you can hear the solenoid kick out but it doesn't turn over. most of the time, if i have help i can hit the solenoid with my maglite and have a friend to hold the key and it will turn over. i can also push it off.
i replaced the starter last week because of this. while i was at it i had the battery and alternator tested and they tested fine. it worked for almost a week and now it is acting up again.
i replaced the ignition wiring last year trying to fix the problem
If you got a new solenoid with the new starter this may not apply.
I was having starting problems with my '87 22RE a year or so ago. Having previous experience with an '81 diesel p/u I knew to check the contacts in the starter solenoid. (there may be another name for them, basically they are the in and out of the electrical path through the starter solenoid and sit waiting until current is passed through the coil and pulls an assembly built around a magnet and holding a copper ring that when pulled into contact with the 'contacts' closes an electric circuit which allows current to pass through the starter motor.) I had watched the auto-electric guy change the contact in the diesel so had a good idea on what to do in the gasser. Yup, contact badly enough pitted to be suspect.
Disconnect the battery before doing any disassembly. It was not hard to take apart the solenoid (I can't remember the details now, but could probably recall if I scratch my head enough) and take out the contact. I had to go to Toyota for the replacement contact (I am in Canada, after-market may be available in the US).
The fix worked for me. The diesel needed contact replacement at about 180,000 km, the gas engine needed contact replacement at about 235,0000.
The symptoms sound like yours - you can hear the click of the magnet assembly being pulled by the activated magnetic field of the solenoid (solenoid = air-core inductor), but there is not always a solid enough electrical contact established between the ring and the contacts. The Toyota parts guy told me that invariably only one contact needs replacement (it should be obvious when you look at them).
While removing and replacing the starter solenoid, take advantage of the opportunity to clean the external electric contact surfaces.
Maybe there will be some other suggestions that pop-up.
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