Car stuck in limp,120A alternator fuse has been replaced what now?

You were very lucky that the majority of the electronic circuits in your Solara functioned at all after a major polarity reversal like the one that occurred when the battery was hooked up backwards. Really, only those circuits that were properly fused would have survived or were supposed to have survived but given the nature of engines and the possible paths to ground, even properly terminated and grounded circuits can be overwhelmed when the battery is reversed.

With that said, it sounds like the control module in your transmission has blown. It was likely taken out when the battery was reversed. You can tell that it is likely in this area by the simple fact that it has gone into limp-home mode and is remaining there.

Have your technician swap out the control module and just to be safe all of the dozen or so sensors that are outboard of it as it is likely that one or more of them was damaged during the reversal. Further, just to be even more on the safe side, have all of the solenoid packs swapped out as well as these electronic devices are not as robust when exposed to reversed polarity and are likely to have blown out as well.

This can be an expensive repair, however, with that said, it is still at least $2,200 less expensive than replacing an entire transmission.