The router is a D-link DIR-615 fw version 3.11NA but this doesn't matter as I had identical issues when using an altogether different router at a previous location; a Linksys though I forget the exact model.
The wireless adapter is a Linksys WUSB600N V1.
Here's my setup and problem in more detail: Internet is accessed via a cable modem, at this point not applicable to the problem I'm having as, again, it happened with another setup entirely. The modem gives data to the DIR-615 router. The router does not matter either, as it continues to work fine and provide internet service to my laptop when the desktop is experiencing the problem. The DNS-323 is connected, via an ethernet cable, to the router and accessed via the local network. The WUSB600N is connected to a USB port in my desktop computer. Mere connection of the DNS-323's cable to the router does nothing in and of itself until the 323 is turned on, where the problem starts.
Once the 323 is turned on, on a regular basis, and completely unpredictable, the wireless connection (only on the desktop - as mentioned earlier, the laptop has no such issues) will no longer allow me to connect to the internet. The wireless connection itself stays connected but I cannot access anything outside of my local network. Again, the wireless connection status still says "connected" with an "excellent" signal but anything outside of local is inaccessible. The main solution to when this happens is to manually disconnect from the wireless connection and reconnect. This will work for anywhere from several minutes to several hours before it happens again.
For what it's worth, the desktop is the only machine that maps the 323 to a local drive. The laptop never accesses it.
Hilaireg, the router does indeed provide IP addresses. Yes, I did indeed secure the wireless to limit access.
Martin