The link you provided indeed does not show the board as listed.
When i look up your mainboard, it also does not list the 3770 cpu as compatible
It only shows the 2cnd generation I7's
Take a look for your self.
http://processormatch.intel.com/CompDB/SearchResult.aspx?BoardName=DQ67SW
It might be that intel just needs to bring out a bios update for you to get it working.
But for that u need to contact intel support.
I chatted with Intel support, and it turns out the i7-3770 will never work with the Q67 chipset. Here's the text of the chat:
Karla: Hello. Thank you for using the Intel Customer Chat Support service. We are glad to be of service. How may I help you? : KArla - can you tell me if the new i7-3770 processor will ever be supportred on the Q67 chipset? And specifically, will that processor ever work in the DQ67SW motherboard? Karla: Hi Bill; since the processor is already launched and no compatibility support was developed for the Q67, this processor will never support such chipset or motherboard. : ok - thanks, thats all I needed to know. Karla: More than glad Bill have a very good day Karla: Thank you for using Intel's live chat. If you are satisfied with our support, please score items with 5 in the online survey that will be shown once you close this chat window. We value your feedback and we will use it to improve our services.
