I've seen default gateways not appear or get assigned incorrectly simply because the routers firmware isn't made to work with Windows 7. Happens here on a daily basis in fact. It might be helpful if we knew which router and version number the OP is using.
Assuming that the driver
is correct the only other possibility is that the router is very old and support has been dropped in which case it can't be made to work properly with Windows 7 "unlikely" or the firmware isn't up to date. Out of date firmware can cause all sorts of problems like dropped connections or default gateway disapearing acts. Windows 7 does indeed know the difference between routers and the firmware they are using.
It's also important to note that disabling IPv6 prevents Homegroups from working at all.
In fact, simply inputting the default gateway manually into the IPv4 properties window has fixed these types of problems more times that I can count. I can post an example of this and how to fix it. This page exists for this very reason. You will need to know what the default gateway is for your particular router in order for the manual input to work. http://pocketpccentral.net/blog/2009...blem-resolved/
IPv6 problems usually only occur on very old routers that were made before IPv6 became standardized "very unlikely to be the cause of this problem". And if that were the problem then upgrading the router to a more modern version would be the best course of action.
Resetting winsock usually is required only when upgrading from Vista to Windows 7 "upgrade install" and in those cases the browsers would not go online at all. Here is an example of what might cause winsock to require a reset. internet connection present, but no browser works.