If your vehicle is showing car won't shift out of first gear, here are the most likely causes and the parts you'll need to fix each one.
Low fluid levels or heavily degraded fluid prevent the transmission from building enough hydraulic pressure to actuate the shift to second gear. This is often caused by a leak or neglected maintenance.
The transmission control module relies on the speed sensor to know how fast the vehicle is moving. If the sensor fails, the computer won't know when to command the shift out of first gear.
Automatic transmissions use electronic solenoids to route fluid and change gears. A failed or stuck 1-2 shift solenoid will leave the transmission trapped in first gear.
If the transmission, engine, or clutch was recently serviced, the wiring harness for the transmission speed sensor or shift solenoids may have been left unplugged, pinched, or damaged.
The physical linkage connecting your gear shifter to the transmission can wear out or snap. This leaves the transmission physically stuck in first gear regardless of where you move the handle.
Severe internal wear, such as burnt clutch packs, broken bands, or a damaged valve body, can completely prevent the transmission from engaging second gear. This requires a major overhaul or replacement.