Q: What will cause an automatic transmission not to shift into the final drive gear? 1993 Buick LeSabre

Hi - by "won’t shift into the highest gear", I interpret this to mean the lock-up of the torque converter, which effectively is another gear (eliminates any slip through the torque converter). Your symptoms suggest that the transmission is not locking up the torque converter clutch. This could be caused by a failed solenoid in the transmission, or the torque converter clutch itself. As for the Check Engine light, a loose battery cable can cause all sorts of weird behavior - get the problem codes causing the Check Engine light first. Most auto parts stores will do this for you on a time-available basis for free. I recommend a transmission inspection performed by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, give you an accurate assessment of damage and cost estimate for repairs.