2001 deville shifting problems

Hey guys newbie here.

I'm looking ay buying a 2001 Deville from my buddy with transmission problems. I did a lot of searching and found this thread. The transmission in this car drives around town fine but when on the interstate it won't downshift when climbing hills. I drove it once around town but didn't pay attention to which gears were working and which weren't.
My buddy said that the dealer told him it displayed a code for a certain solenoid in the transmission but he couldn't remember which solenoid. I can go drive it again next week and also pull the codes but I was wondering how I might determine if it is a shift solenoid or one of the others? I know sometimes codes will store for one problem but that isn't necessarily the actual issue.....it might be something else causing that to malfunction.
He wants $800 for the car and I plan to do the work myself. If I can put under $100 in parts to the transmission I'll come out pretty good. The rest of the car is in pretty good shape. It has 202k miles though......
I'm hoping I can get away without having to buy a used transmission for $500+

What are your thoughts?

nate

Update:

My good fortune is definitely over with this car. driving home on Friday it went well until I got off the interstate and onto the secondary highway where I immediately climb a big hill. The car acted like like it didn't want to shift down and started hurking and jerking and went into limp mode. About this time the engine started to overheat a little too. The RPM's were all over the board during this whole time. I also had my 2nd flat of the day at this same time......
Anyway, I got a ride back to town to fix the tire and when I came back things had cooled down a little and I was able to accelerate to about 64 mph before it went back into limp mode. This morning I attempted to drive it back to town after clearing the codes and letting it sit all weekend and I wasn't able to go a mile before it started all over again. Following is a list of codes that I pulled on Thursday and then cleared, and then another list I pulled this morning and cleared. Does this sound like a failed TCC solenoid or does it sound like transmission replacement time? I'm fine with either but I need to get started ASAP as I'm losing my shop access in a few weeks. TIA

Thursday codes:
P0140
P0141
P0741
P1415
P1567
P1860

codes set on Friday:
P0742 - TCC circuit stuck on
P0733 - INCORRECT GEAR 3 RATIO
P0732 - INCORRECT GEAR 2 RATIO
P0404 - EGR FEEDBACK SIGNAL OUT OF RANGE
P0137 - O2 SIGNAL LOW
P0036 - HO2S HEATER CONTROL CIRCUIT B152