Chrysler Repair: 99 Chrysler 300m transmission issue, imscared, speed sensors

Question
Ok let me start by saying thank you for your time to read and possibly answer my question. I have a 99 Chrysler 300m and I just actually bought the car. Upon driving I noticed the car would not shift out of 1st gear even when I tried shifting with the auto stick it would not move from the 1 box on the dash. Also I really don't think that your suppose to be going 40 mph at 3000 3500 rpm lol. Well anyway I read a little online and it said something about changing out your input and output speed sensors, so I did that no change. I even changed the tranny filter no change. I don't think it's in "limp mode" cause it's not stuck in 2nd and even if I reset the TCM or the computer as soon as I start the car it's still the same. Now I tried pulling out the TCM shutdown relay to see if changed anything and it didn't it acted the same way as if the relay was plugged in. I also read about tranny solenoids going bad but it doesn't show any signs of erratic or shuddering at all. It runs and drives wonderful in 1st gear and thetranny doesn't make a sound at all even shifting into reverse works great no sounds or issues. I am on a limited budget I have 3 little children and imscared to take it to a transmission place cause there answer is always oh you need to replace the tranny. Do you think it could be a bad TCM ? Does it automatically shut down when the car starts so then it won't shift out of 1st gear? Idk I really need some help here.

Answer
Very few conditions exist that would put the transmission into limp mode that will not generate any fault codes. No power to or from the transmission control relay would be one of them. So we'll start there. You'll need to check the related circuits. If you haven't done so already, check all the fuses in the fuse box under the hood. If they are all good the next step would be to check the transmission relay power feed, ground a output circuits. Remove the relay and check for power, with the key on, at cavity A and B with a test light. The test light should illuminate on both. If it doesn't light up at A, power supply and grounds at the TCM will need to be checked, as well as the wiring to the relay. If B does not light up, there is an internal problem in the fuse box. If OK, connect the test light clip to the battery and check the other two cavities. If the test light fails to light up you'll need to check the ground wiring as well as the wiring to the top of the transmission for an open circuit. If the test light shows that all circuits are good then you're looking at replacing the solenoid pack in the transmission. Post a follow up with your results.