Hello and welcome to Just Answer!
The o/d is electronically controlled and usually when there is a problem it will set a fault code in the PCM. Have you checked the PCM for fault codes?
Fault code P0123 will affect it from shifting into o/d. This code sets when the throttle position sensor signal voltage goes high. This could be cause by the TPS, wiring problem or a PCM issue.
Have you replaced or checked anything yet besides the oil and cable?
Is p0123 fault code still setting after you have replaced the tps and disconnected the battery?
Sorry for not getting back to you sooner, I fell asleep last night. I am a full time tech during the day and will be online after work, so I will get back to you then.
Do you have access to a scan tool? I would like to know if the PCM is allowing o/d. If the PCM shows allowed, that means it's commanding o/d and the problem is from the PCM to the o/d solenoid, or an internal transmission problem. It could be the PCM, wiring problem, o/d solenoid or internal failure. If the PCM shows the o/d is not allowed, then there has to be an input to the PCM that isn't working properly.
Does the transmission have 1st, 2nd and 3rd gears?
Do you know what the engine rpm is when traveling 60 mph?
Then it can't be shifting into third or overdrive. The RPM is extremely high at 60 mph and I am not sure what the RPM would be if it stayed in second. I don't think the RPM would be that high even if it stayed in second but I would like you to try and see if it feels the same if you drive it in manual second. Pull the shifter into manual second and let me know if it's the same.