Wireless network connected yet firefox, IE7 won't connect

My home wireless network is connected at excellent signal strength, and the other computer on the network can access the internet, but once or twice a day, none of the browsers on my operating system can load anything until I restart. Also, TrendMicro can't update until restart.

Possibly related:
The last time this happened, I checked task manager and found two copies of rundll32.exe, but only one copy once I restarted. The computer was nuked about a month ago, I've kept my user privileges to the minimum and I perform frequent updates and scans, so a trojan seems unlikely, but maybe it's a driver problem?

Also, on one occasion the wireless showed limited/no connectivity, but this is not usually the case.