It may be in "limp home mode" When the computer sees a problem it will sometimes lock the trans in second gear as that is a gear you can get home in. The car will start from a stop and give you about 30 mph. If you don't have the ability to communicate with the on board computer to check for codes and clear them you may try disconnecting the battery to see if the trans computer resets and it may shift again. That said, the fact that it may have gone into limp home mode indicates you have some type of transmission problem, perhaps a solenoid as you suspect.
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