I copied this from the
www.automotiveforums.com on the P0773 problem, but I do not think that the solenoid problem it calls out could cause the car not to start. Have you taken it to a auto parts store and had them read the codes for you. It is usually free and they will explain them also.
Background (from the FAQ thread):
Solenoid E (SL) is the
torque converter lock-up solenoid. If the torque converter is a little slow
locking up, it will set a P0700 code.
The ECM compares engagement condition of TCC with lock-up
schedule in memory to detect MECHANICAL trouble of lock-up solenoid, valve body
and torque converter. (The P0773 trouble code is probably from monitoring
electical signal to the solenoid. Might be worth checking the electical
connection and wiring before you replace the solenoid) A P0700 trouble code is
set when TCC lock-up does not occur during appropriate speed, or lock-up does
not release at appropriate speed.
There
are simple electrical tests to check the solenoid and plunger but the
transmission pan must be removed to gain access.
A Toyota
service tech can check the system without pan removal with his analyzer.
Keep an eye on the rpms when you are above
50 mph. They should be constant at constant speed, like in a manual transmission
since the torque converter is supposed to be locked up above this speed. If the
torque converter is not locked, then your mileage will suffer, and your tranny
fluid will heat up above normal temperature. If you use synthetic fluid, you
will minimize the problems from overheating the fluid. The life of the fluid
will be shortened in any case if the torque converter doesn't lock up and you
drive at expressway speeds, particularly in hilly country.