Also, Firefox seems to be slower than before I upgraded to 6.0.2.

Upgraded to Firefox 7.0.1. Still same problem - slow connection to websites and dial-up disconnection. No apparent problem when not using the browser.

Upgraded to Firefox 8.0 . . . dail-up lasting a bit longer, but still disconnects.

It seems like nobody is able to help me.

Perhaps the Firefox developers don't care about dial-up users.