ok..... let's try to eliminate what's wrong...
when the CP top is by itself, everythign works fine...
when CP is placed on the box (where it should be...) then player 1 RIGHT direction doesn't work... everything else still works fine.. right ??
ok... you have concluded that there's is no pblm with the wires... (so... when the CP is placed against the box.. the wires didn't come loose... )
now.... player 1 is on the left side... and right direction is the left most switch....
when you put the CP on the box.... and when you click the directions... do you still feel the click on the microswitch ??
I'm asking this because it might be that the wires are all good, but when the CP is tightly fitted... somehow.. the stick is blocked from going all the way left (the bottom of the stick... I mean)... and not able to click on the microswitch ??...
(if you're using 360 stick or something special... then its different story...)
as others have said.... a few pics would help us spot what's wrong....
photo the top of the cp, the bottom of the cp, and the box, and the cp on the box (when it doesn't work...) and lift it up a little and take a pic on the gap... and so on...
good luck...