Hmmm, with mine, i had it 2 ways.
First i had a scart splitter and put them all into one, hooked up to it.
Second way i had it direct from the tv, and my cable box and dvd and tv worked ok with it.
Cant understand whats up with yours.
If its a 2 way scart check its on output.
By the sounds of it though, it seems you havent got your cable going innthe right places for all your equipment.
When your dvd player gets no pic, try switchong channel to AV or another one.