It sounds like the T catch in the lens is maybe broken, or you're misunderstanding the camera and it's working properly. Do you have another lens you can try it with? The body shouldn't click though...
The order of operations (and sounds) is:
- choose a fairly-high speed on the body speed dial, or even the orange-dot mechanical mode
- insert cable release into lens
- slide switch to T (it must latch in the T position!)
- fire mirror from body, wait 5s for vibrations to stop
- fire lens from cable release (one "ting" of shutter opening)
- wait a while
- put on lens-cap (prevents you bumping camera while closing shutter)
- return switch to N (one "ting" of shutter closing)
- crank
Note that the small noise of the shutter opening is pretty similar to the sound of the shutter at 1/400 - have you taken the back off (use M mode to fire the body) and looked through the lens to make sure that the shutter really isn't staying open? Note that the shutter closes when you slide the switch back to N so if the switch isn't latching properly, you'll not get a T mode. The T switch is a purely mechanical thing that holds the shutter open with no electrical power for as long as you want.
The camera body connects to the lens electrically (except for the 1/400 mode); it provides voltage to hold the shutter open for the right amount of time then withdraws it at the end of the exposure. If you're using T mode, the lens just stays open and ignores the end-of-exposure signal from the camera. Dirty electrical contacts etc will have no effect on T mode. This also means that there is nothing mechanical happening inside the body at the end of the exposure selected on the body-dial, which leads me to believe the click you're hearing when you slide the switch back to N is actually the shutter closing, and that it's maybe working properly.