2001 GMC Sierra won't shift out of 2nd gear

Hello, You could be looking at a bad shift solenoid, slipping clutch-pack, blockage, a bad tranmission position sensor, or a bad valve body leaking hydraulic pressure for 3rd gear. The 4L80e is a solid transmission, but clutch packs wear out, especially with towing, and the solenoids are known to fail given enough time. Of course, the fluid level could just be low, but I would not count on it. There are several other issues that can cause this issue, even the vehicle going into limp mode, so diagnosis will need to be done. The good thing is that every transmission shop in the country has seen thousands of these transmissions, parts are cheap, and it is a simple transmission to service.