To me it looks like your Denon 1600 is a progressive scan player which means it will only output 480P. So changing cables will not somehow magically scale to 1080i, you will need an upconverting DVD player like the Oppo 971, 981, Panasonic S-97 or S77, Sony DVP-SA70, etc.

If you like your current setup, then no worries. If you want more, then get the Oppo you mentioned and either run straight component or get an HDMI-component cable.

Bottom line is you cant get HD display without the use of an upconverting DVD player(or blu ray, etc) to generate it.