I notice you said there were “codes” generated by the problem. Can you give me a list of those codes?
There are many reasons a car can go into limp-home mode. As your scanner told you, one or more of the solenoids could be bad — did you replace both solenoids; there’s one on outside of the valve body and one on the inside. Usually, the solenoid on the interior of the valve body handles gears 1 and 3, for instance, while the one on the outside handles gears 2 and 4. I won’t say that it is a universal template for the industry, but, by and large that is the way things happen.
With that said, it is quite likely that the other solenoid, the one that apparently wasn’t replaced, may have been the one that failed so the Solara will remain in limp-home mode until the device is replaced.
The solenoids aren’t the only reasons for a vehicle to go into and remain in limp-home. Indeed, it is possible that one or more gears has or is failing. That is a condition that would generate a limp-home command from the engine control module (computer). Another condition that could generate a limp-home command is a failing clutch pack or packs, or a failing band or bands.
In addition, the problem could be one of the many sensor packs or control modules that work with or in your Solara’s engine bay. Among the sensors that could be failing are the throttle positioning sensor, the mass air flow sensor, the mass air pressure sensor, a temperature sensor and others. There are at least a dozen sensors that work with either the engine control module or the transmission control module (it could even by the TCM) and there may be as many as 8 or more control modules and which may be at fault.
For my money, I would have the other solenoid replaced asap as I think you will find that once the second one is changed out that the code will go away.
Please let me know the outcome.