OK, first off, do update your drivers. It turns out that my old Intel 2200BG wireless not only supports the faster 802.11g wireless, but they also support WPA2, which provides better security.
Wireless routers come configured for maximum performance. This is a good thing, but it does not have anything to do with your environment. So, all of these parameters can be changed. Usually changing them results in a performance difference of .001 millisecond- so no harm no foul. In order to keep the broadcast packets from ever interfering, a simple down step in a couple of parameters on your wireless router will fix the issue.
What needs to happen is that the router's settings need to be changed so that the window for getting duplicate or overlapping signals from multiple wireless computers can't happen. Basically, we are setting the router up to generate a little bit more traffic by shortening the size of the packets it sends and also by having it require the wireless computers to check whether or not the network is already busy a little more often. Technically, this will reduce the performance, but you probably will never notice it with the small changes we are making.
The settings you want are Fragmentation Threshold (it might be called something else, but it will be close enough) and RTS. Fragmentation usually comes from the factory set at 2346 and RTS comes at 2347. Change the Fragmentation to 2306 and the RTS to 2304. That might do it. In order for this to work, your wireless cards must be set to RTS, not CTS, in their configuration- or they will ignore your RTS settings.
If not, change the Beacon, which usually comes at 100, to 50. The Cisco guys that work on large enterprise networks are having a stroke right now. Just give them some oxygen and keep going. Changing this increases the "noise" on your wireless network. On a big network, the congestion could be overwhelming, but since we are talking about small networks with less than 10 devices, it won't matter.
Now, your wireless network should work smoothly. If not, keep tweaking the Fragmentation and RTS numbers down. Always keep the fragmentation number 2 higher than the RTS number. Remember small changes make big impacts with these settings, so don't go crazy. If it isn't working by the time you hit 2200, this probably isn't the problem that you are having. Put your settings back at the default numbers, go back to troubleshooting and find a different solution.