I have not replied yet as I don't think I can diagnose your problem. However, this information may help you.
2000fcw have no electrical connection between the lens or film back, the communication is purely mechanical. The "C" mode is also purely mechanical, as it works with no battery installed. The B and all other shutter speeds require the battery to trip both shutter curtains.
Thus if the camera works on "C" but not the other modes, the likely place to look is the power supply, and very rarely the electromagnets that trip the shutter curtains. The power is easy, and the 2000 series bodies use so little power that a mostly dead battery will usually work fine. Electromagnet failures are very rare, and not repairable (no parts available). However, if the shutter fires correctly with the lens removed, the electromagnets are probably fine.
The lens couples with a rotating key that arms the shutter and closes the aperture. If the mating part in the lens is stuck (ie: will not complete the aperture cycle), then that can halt the mechanical process in the body and not allow the camera to get to the point of triggering the shutter.
The 2 mechanical connections to the back is the winding gear and the dark slide shutter button block. Since you can trip, or start the shutter tripping process, the dark slide interlock is probably OK. The back wind mechanism may be jammed, but those symptoms are not what you have described.
Best I can advise it to take it to someone who understands the mechanics and interlocks on the body, and they can then tell you if it needs servicing.