Which wired remote did you get? Does it have a connector compatible with the D3100's accessory port on the side of the camera.
I too have now looked at the D3100 manual and it doesn't look to be capable of even using Nikon's wireless IR remote the ML-L3, let alone a wired remote.
There is no shutter mode setting for remote actuation of any sort, that I can see, only a self-timer.
My remote is Shoot MC-DC2, i got it from amazon for £4, I am asking for a new one, i think it is not functioning....
I too have now looked at the D3100 manual and it doesn't look to be capable of even using Nikon's wireless IR remote the ML-L3, let alone a wired remote.