It could be a bad NIC or port on any device causing issues that keep the network down. A bad connection, for example, might keep a switch cycling in trying to add the port to the active list. Are you seeing any indication of flooding or overload (some routers or switches have a collision LED)?
If you are pinging by computer name and you don't run your own DNS, it could be a problem with the local MS Browse Master computer negotiations. I'd try turning off the capability to become a Browse Master on all machines but your HS (statically-addressed) machine. The Browse Master is the machine that maintains the network list of all machines on the network. When machines are turned on or their network addresses otherwised changed, the machines will talk to each other to determine which is to become the master browser to hold the network list. This takes a minute and then it may take longer to populate the list to all machines (several minutes).
It could also be a very short DHCP lease, or a competing DHCP server (did you leave the old router on and hooked up?). To get around this possible problem, put static IPs on all machines and shut off the DHCP server(s). Also, in tests, always use the IP address for pings, etc. It avoids the name-to-IP conversion issues.
If you want, load up Ethereal on one of the wireless machines and save a capture file around the event. That may see something that would tell us the problem. I can interpret the capture for you if you wish. Promise I'm a white hacker! ;-)
Even though you don't see another wireless network ADVERTISED, it could still be there. Best to make sure all your machines can only connect to YOUR wireless network and that you've changed all the settings so your wireless network is different than any other. And yes, it could be a 2.4GHz device interfering, such as a wireless camera or phone system (CyberGenie).
And finally, it could also be spyware, virus, trojan, etc. Make sure you are up to date and scan everything.