When I put the car in drive with the shifter or any other mode it won't seem to change anything, only when I put it in 1 and step on the pedal there seems to be a different response. Nothing happens to the rear wheels though, while I can see the cable changing the position on the switch on the transmission itself. You guys have any idea what might be the problem?

PS: Please bear with me, this is my first engine swap and I don't know about the condition of the tranny before the swap.

Somehow transmission oil was at an all time low, strange, didn't leak all that much. Refilled it, and I put the car on jackstands, rear wheels will move now although at a very slow pace. Must have something to do with the engine running bad again, soon a specialist will come by to set the ignition and everything perfectly and get the engine running properly again.

Transmissions' TV cable (Throttle-Valve) adjustment writeup is on thirdgen.org here: https://www.thirdgen.org/detent

Thanks, man! Still not sure about the state of the transmission, but the car is at the (American car) specialist's place now, he's letting me work on it there with his guidance and help, really great. We should have it all figured out in no time! He said we should be done tomorrow.