A kick down cable is lame men's terms. TV cable is the normal name. They are the same thing. TV is Throttle Valve cable, when it pulls it moves parts in the trans to direct fluid to the proper places with the throttle valve. Basic as I can explain, I'm starting to learn more bout transmissions. So kick down and tv are the same. I had a TH350 and now I have 700R4, the kick down on the 350 and the tv on the 700 look almost identical.
Kevin, That is not accurate. On the TH350 as the OP has, the kickdown cable only "goes along for the ride" as the throttle is opening from idle...doing nothing until full throttle is reached (assuming it is adjusted correctly) & then commanding a 3rd to 2nd downshift. A TH350 transmission does not need a kickdown cable to operate, drive, shift, ect. the only thing missing would be the automatic 3rd to 2nd downshift @ wide open throttle only...the trans can/will last just as long without a kickdown as with one...has NO effect on any other function.
Now the 700r4 TV cable is a completely different animal...it needs to be in place for the trans to work, shift & LIVE. The valve is moved as the throttle is opened/closed
To the OP, I would suggest you unhook the kickdown cable from the carb to take it out of the equation during your testing & set it properly after you have figured out the problem. My first thought would be to look for either a bad vacuum hose on the modulator or a bad modulator. The problem could also be with the governor, so I'd look at it after checking the modulator. Good Luck, Hope this Helps, Lorne