I saw the exact same issue on my DMA2100 before I sold it - went to power it on one day and got the blank screen after it booted up. In my case you'd see the WMC logo as if it was going to go into the menus as normal, only to get a blank screen thereafter. Only fix was to delete and re-add it to WMC, but problem came back again after a couple of days. Tried all sorts of stuff to fix it (short of completely reinstalling the PC which I didn't want to do), but nothing worked so I got rid of it. No network changes for me btw.
I don't think the issue was with the Linksys, and neither of my two 360s had any issues at the same time. It's something getting screwed up in WMC as best as I can tell.