Cam Position Sensor
I had this same problem when I first bought my Supra. I could crank it for hours and it would never start. The problem was the cam position sensor, which had nothing wrong with it at all. Its the connection and/or wiring harness. Our cars are old and the wires become weak an brittle over time PLUS the wires for the CPS run right over the head...bad news bears.
My temporary fix was to disconnect CPS connector, clean, re-attach, and make sure it had a good connection...well that didn't work. Next I simply just took the wires that ran over the head and gave them a good jiggle/shake and boom! Started right up. Later I did re-wire it and no problems since. Hope this helps.
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Zach
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