If you can still send and receive mail while the browser is on strike, it's not the internet connection itself. Changing filters and wiring is not likely to fix it.
If this is a Windows machine, take a look at the logs to see if it reports what the error is.
Control Panel - Administrative Tools - Event Viewer.
Then look at Administrative Events (scroll through). Ignore ones marked "Information", look first for red ones, and if there are none of those, look at the yellow ones.
Don't panic at the apparently large number of these things - some of them are generated by stuff outside your PC.
You'll probably find something that uses Internet - type words such as DHCP or IP.
You can usually click on a link that will tell you the next thing to try.