Here are the most likely culprits:
* Transmission Control Module (TCM) or PCM (Powertrain Control Module) Failure/Malfunction: The TCM (or the PCM, which often incorporates TCM functions in this era of vehicles) controls the shifting. A faulty TCM/PCM could be sending incorrect signals to the transmission, preventing upshifts. The check engine light is a strong indicator of this. A diagnostic code read is absolutely necessary.
* Wiring Harness Issues: There could be damaged wiring between the TCM/PCM and the transmission. A wire could be shorted, broken, or corroded, interrupting the signals needed for proper shifting.
* Transmission Range Sensor (TRS) Problems: This sensor tells the TCM/PCM what gear the transmission is in. A faulty TRS could provide inaccurate information, leading to the transmission staying in first gear.
* Speed Sensor Issues: The vehicle speed sensor (VSS) plays a crucial role in determining appropriate shift points. A faulty VSS could cause the transmission to remain in first gear.
* Incorrect Programming/Calibration: In some cases, the TCM might need to be programmed or calibrated specifically for the vehicle and new transmission. Failure to do so after a transmission replacement is a major error.
* Fluid Levels/Quality: Even though the transmission is new, it's worth confirming proper transmission fluid level and type. While less likely to be the primary issue, an extremely low level *could* cause problems.
In short: Get the diagnostic trouble codes (DTCs) read from the PCM using an OBD-I scanner (for that year). The codes will pinpoint the most likely cause. Ignoring the check engine light and assuming it's the new transmission is a costly mistake. The problem is almost certainly something electrical or a control system issue related to the installation or pre-existing conditions.