The OP mentioned using the cable that came with the camera ... so shouldn't be any problem there.
Sounds like something is brock ... maybe the cable is frayed inside or something?
If you can pick up u 3.5mm to dual RCA cable/adapter, try both the red and white plugs in your TV's video in and if neither work, I would suspect the camera itself ...
Not always true. the 3.5mm plug has been modified many times where the spacing between contacts lead to different wires.

