The Motorolla SBG-6580 is not a modem, it's a gateway (modem+router combination).
Why do you want to use the DGL-4100, as opposed to just using the router function of the Motorola gateway? Looking at the spec's it supports dual-band wireless-N and has 4 gigabit Ethernet ports, so it seems like it should do what most people would need from a router.
Have you tried to disable the routing functions in the Motorola and bridge it to your DGL-4100?
Have you tried setting the DGL-4100 up as a DMZ device in the gateway?
Have you resolved potential IP conflicts by changing the base/DHCP address of one or the other device? If I was a betting man I'd put my money on this, since both the D-Link and Motorola default to 192.168.0.xxx, which means they are both trying to use the DHCP address range of 192.168.0.1-255 (hint, to use both together you should change one to use a different DHCP IP range, like 192.168.2.xxx).