Your Canon EOS lenses won't work with the Nikon.
Your Canon 35mm lenses (if autofocus) should work with the Canon digital. The bold text was copied off one of the Canon camera forums on google and pasted here. the third generation lens, however, came with the advent of autofocus, and the mechanical linkage was replaced with electronic controls. non-autofocus lenses cannot be used on an autofocus body, and vise versa.
The best advice would be to write down which lenses you have with the model numbers & post them here so some of the experts can answer, or call B & H photo and ask one of their experts if you don't have a local camera shop you can go to.