The lack of self cancelling on the indicator may be a red herring.
First try the indicators in both dirctions whilst turning the steering wheel one full turn and back. Ignore the position of the steeing wheel for the moment, we want to establish if your indicator will self cancel in any position.
If they do indeed self cancel in both directions then experiment with the steering wheel position to find the middle point between the two cencellation points. This will tell you where your self cancelling cam is located on the column.
With the steering wheel removed you'll see what looks like a chisel mark in the top of the column. With wheels pointing straight ahead this should be in the 12 0'clock position (6 o'clock for RHD)
If it's not somewhere near the straight ahead position then the likelyhood is that your steering column is not correctly aligned with the box and rectification involves seperating the box from the column, inserting the centralising pin in the box, getting an assistant to hold the steering wheel (column) in the correct position and then re-installing the box.
If you get this right and you find that you do not have an equal number of turns from centre to both left and right then the pitmarn arm on the box has been mounted incorrectly.