Hello,
Just for information, IF you don't get pimple configuring a normal DIR-600 router  

 :
You may want to convert your DIR-600 router in a Wi-Fi Repeater-Bridge, which will allow you to connect both networks together ; BUT 
in the same range of IP addresses...
For this, have a look at DD-WRT Web site to get their special firmware for the DIR-600.
I tried it already, it works well on my second DIR-600 router. 

A good advice:  don't use Internet Explorer but FireFox with (defaults settings out of the box) to avoid problems in case you want to come back to original firmware from D-Link.
Hope this will help.
Regards,
HP
P.S.Do NOT rush AND Read Carefully the dedicated pages for DIR-600 from DD-WRT before to change the firmware.
It is not complicated to do if you know what you are doing. So, always use your brain first.  
