Thought this would be a fairly straight forward fix of making sure that the transmission fluid was full with no air in it, as well as a few other things to try.
Well, I’ve run out of things I can reliably try right now. Replaced the output sensor on the transmission, filled the transmission fluid with the proper type, read error outputs. (boy was that odd, you have to turn the key three times in a certain way and it blinks codes out at you)
The error readouts point to an Oxygen sensor, and the speed sensor. The oxygen sensor I could care less about at the moment, as I can’t really reliably drive the car in first gear. Once it shifts, then I’ll fix that, otherwise its wasted money as I won’t be driving anyways.
Any suggestions on things to try? None of my local mechanics have a machine to read or program this thing by the way, so that is kind of out of the question.
Report the specific codes. “The speed sensor” doesn’t say enough. You replaced the output sensor - why that one and not the input? (There are two of them).
Its probably stuck in second and stuck there because of that. Electronically speaking trying to figure these things out without a scanner is a nightmare. Call locally owned transmission shops - general mechanics won’t do this kind of stuff. Someone who specializes in transmission should have a scanner to put it on. If you pay a little bit of time for that you’ll probably be back on the road much faster and with less aggravation than otherwise.
The OP says it “won’t shift out of first”. Maybe he just can’t tell the difference.
Could very simply be stuck in second, since I hear that is the gear that it will get stuck in when in limp home mode.
Will try to find a transmission shop locally. As far as I know, there aren’t any where I live. Funny thing with this car, is the codes are output by blinking a certain number of times when you hit the key three times. Will try and read the codes again before posting back. Could be the out speed sensor, as that is the one I couldn’t replace as I ran out of money. Thankfully a new job is on the way, so I might have funds again. 
Error codes are as such:
37 - solenoid error (says no limp-on triggered from this)
15 - speed sensor (located on top of the long casting near the right axle on the transmission, the one we replaced was near left axle)
21 - oxygen sensor (if I can’t drive it, I don’t really care)
55 - no more error codes (basically tests done)
The check engine light will only flash PCM faults, you will need a scan tool to read Transmission control module faults.
Alright, I guess I should start trying to find a transmission shop in the area. All the car guys I ask in the area say there isn’t anyone good with transmissions around this part of NY though.
I’m assuming any speed sensor issues wouldn’t lock the car into limp-home mode, as the manual doesn’t say speed sensor errors trigger this. So the most important part is purely transmission reading.
An input or output speed sensor failure will cause the transmission to go into limp mode. As cigroller said you should replace them both, they are cheaper than a diagnostic test ($20 each). These are on the side of the transmission that faces the radiator, (you may have replaced the vehicle speed sensor near the fire wall).
The speed sensor error will put the transmission in limp mode. Neither the TCM not PCM know how fast the thing is going. Is your speedometer working?
Here’s a handy page for you to check out: http://dodgeram.info/Engine-Gas/OBDI/Fault-15.htm Its a Ram truck page, but its the same thing.
The 37 is actually for part of the torque converter clutch circuit & I’d bet this would also send it to limp mode.
Before anything else I’d do a good inspection of the wiring harnesses - perhaps try to come up with pinout diagrams for the TCM & transmission connectors. Also find the transmission’s main ground strap, check it out, pull it off, give it a good cleaning & reattach.
Speedometer does not move (at all). I’ll look into the other things as funding increases.
Thanks
update on the 10th
Went to a transmission shop this morning, found one online. The speed sensor won’t read on my car, so either the wiring harness is shot (more likely) or the other speed sensor I didn’t replace is bad. Shop says its not making a circuit, so the sensor won’t read.