My Kenmore 70092991 clicks but won't engage the motor. I replaced the thermister and the thermal fuse (I didn't test in advance of replacement thinking I knew what was wrong) and that didn't fix it. When I tested the parts they were fine.

Only a few of us would know this is a dryer. http://www.searspartsdirect.com/partsdirect/part-model/Kenmore-Parts/Dryer-Parts/Model-11070092991/0582/0151200?searchedModel= 700.92991 &blt= Confirm power is actually reaching the motor when you turn it on. I am sure power is getting to the switch but maybe no further

Are there any fuses or switches that would trip to prevent power from gettong to the motor would be the question I'd have to answer next...

High temp limiter and thermostat are normally the only units that would stop power. Just clicking could even mean the motor itself has failed.

When I do a power continuity test on the control board (touching one pin of my reader to the motor contact on the control board and touching the other pin of my reader to the door contact) I get no VAC reading. The tech sheet says I have to replace the control board.

I have a hard time believing that because I have two control boards and neither of them work.

You say it could be a motor problem. How would one test the motor with a VAC/VDC meter ?