Network, no internet

I have a home network set up with two computers hardwired into my 4-port wireless-G LinkSys router. In addition, I have 3 computers connected wirelessly (with USB wireless-G adapters). These wireless computers intermitently lose connection with the internet; the message I get is that the computer *is* connected to the network, but *not* connected to the internet. What up?

Do I have to power-cycle everything to get them back? Can I not troubleshoot them one a time?