Sounds like you want to "hang" an AP onto your wired system to extend
coverage. In this case, your new DSL router will serve as the AP.

You would need to first go into the G604T's interface (connect a
cable from pc to it's LAN port) and assign it a LAN address within
your subnet, but different from the DI-624. Outside of your DHCP
range on the DI-624 also. Turn off DHCP on the 604T. Assign it's
wireless to a different, distant channel so the two don't interfere.

Then connect a cable from a LAN port of your 624 to a LAN port (not
WAN) of the 604T. The 604T should now act as an AP. Once it works
ok, setup security.

There are more details that may or may not snag you depending on what
you know, but that's basically the approach.

Steve