Transmission wont shift out of second gear

depends on model year but yes speed sensor on wheel could also

transmission clutches bad for third gear operation. needs trans overhaul..

Bad valves or possible bad speed sensor.

I'm thinking straight up, just too many confusing answers. If your engine light is on then of corse their are allot of possible problems. Your throttle Positioning Control Sensor gone bad can cause the trans to not shift or not shift right and will cause engine light to be on. Then possibly Bank 3 Oxygen Sensor has gone bad and can cause the ****** to never come out of 1st gear. Always have your sensors tested first before buying cause of corse, they are non-refundable.

have you tried shifting with the car stopped not running does it shift easy or hard sometimes the syncro inside the trans gets worn or the shifter fork could be bent damaged usually a trans shop or specialist can help you work on it because its a big job tom pull out the trans and tear it apart but if you want to do it yourself its possible

Did you scope the TPS Sensor?

Did you use old trans sensors
That may have been your only problem

Just saying ,won't even guess,speed sensor maybe

did you have pinion factor and quick learn performed on the trans module after replacement? if not then the trans won't shift correctly. also is the check engine light on with any engine codes in memory? the engine module may the trans stuck in limp-in mode(2nd gear).

your shift silinoid is gone there is 2 inside the transmission

If it has alot of miles on the trans its possible the sun gear is shot. It will work in 1st and 2nd but forget the rest. Get a trans out of a junk yard my truck had that problem and it was the sun gear. That's what the trans guy told me so I got a trans with about 40,000 on it since mine had 180,000 on it when it went.

check or replace your thottle position sensor tps that trans needs to know where the throttle is to shift if it is bad it will do as you say wont shift to third
another telltale is it will act like it goes into lockup when shifting into reverse and stall the engine