Well I checked everything out, and it turned out to be the lid switch! Apparently the lid lock is more than a solenoid, because I manually moved the lid lock (wasn't locking) and that along with the lid switch depressed, the washer kicked on right away and has run through all the cycles. So I guess the lid switch and the lid lock both serve as limit switches that both have to be operated in order to activate through the middle of the wash cycle, and to continue throught the rinse and spin.
Thanks for all your help with this, it is greatly appreciated!! If it wasn't for the manual and the troubleshooting flow diagram, I probably would have spent the money for a new timer when it wasn't needed.