This might be helpful to someone.
I just installed this router (DIR655) and after the standard setup, everything was working except for local-network machine-name resolution. I first noticed when my web applications were not able to connect to the database server:
Microsoft OLE DB Provider for SQL Server error '80004005'
[DBNETLIB][ConnectionOpen (Connect()).]Specified SQL server not found.
Pinging a local machine-name would return errors like:
Name resolution for the name [machine-name].hsd1.or.comcast.net timed out after none of the configured DNS servers responded.
So it was obvious the routing was sending my requests *out* to the ISP.
After digging around I found that "Advanced DNS Service" was enabled, (Setup > Internet > Manual Internet Connection Setup > Advanced DNS Service) which I presume was by default since I just set this up. Disabling "Advanced DNS Service" solved my problem, and I was once again able to connect to local network machines by name using Remote Desktop, and via web applications using SQL Server connection strings that used server names.
I also learned through this process that between my old DLink router and this one, that DLink has changed their customer support to some overseas provider. After 4 separate phone calls, I was unable to get 1 person who could clearly repeat back to me the problem I stated to them, repeatedly. ("I can't connect to another machine on my network, by name") Each of the heavily-accented people I spoke with seemed ill-equipped to help with anything more complex than "How do I plug this thing into my computer?" sort of questions. So, good luck if you ever have to call them for help.