This may help picture the situation in series. Trace the route to from
my home desktop:

iznogoud at bigpapa:~> traceroute
traceroute to (, 30 hops max, 60 byte packets
 1 (  10.194 ms  11.361 ms  11.557 ms
 2 (  12.180 ms  12.380 ms  13.147 ms
 3 (  27.331 ms  27.768 ms  31.007 ms
 4 (  31.311 ms  31.733 ms  35.064 ms

The first is the D-Link WAN. The second is the, which is
the modem+router LAN, and this is also the gateway address of the D-Link's WAN.
The D-Link's WAN has an IP like or something like that.

Say the WAN of the DSL-model+router dies. The D-Link will have the 192.0.1.*
link dead, but the 192.168.0.* network will work just fine. All your computers
will live in that network and will work fine.