[EDIT]Removed some crap after rereading the original post[/EDIT]
Hm hm, it sounds like you need to reconfigure the D-Link router to get it working properly.
Unfortunately I have no experience with D-Link 704-P, but surely it should be able to handle DHCP from the cable, and static IPs for the LAN... I guess it's time to consult the D-Link manual or something :-) Keywords to look for: IP MASQ, NAT.
Once you get this going, you should be able to turn off the DHCP from the PC again (if desired).