Click the orange Firefox button, go to Options | Options | Advanced | Network (tab)| Settings (button) and click the option at the top called "No Proxy".

See also Network Tab

Another setting which might cause a problem can be found in the General tab in the Advanced menu. If "Tell websites I do not want to be tracked" is enabled, remove the checkmark to disable it.

OK, the "Tell websites I do not want to be tracked" option was not checked, and I ticked the "No Proxy" option in the connections tab, and Firefox still wouldn't connect to the web. However after trying to reconnect to the web I went back to look at the "No proxy" setting, and it had unticked itself, and I confirmed the unticking process by reticking it and again trying to reconnect to the web, and it once again unticked itself. Is there a ghost in my machine?!

I forgot to mention that I created a Windows restore point before I upgraded to Firefox 4.1, and after having the connection problem with 4.1 I restored my OS to the prior point, but my Firefox behaved the same way and wouldn't connect to the internet like it used to.

It sounds like the link between the modem and Firefox has gone pear-shaped somewhere. Does the modem have an internal firewall?

As regards System Restore, I'm afraid that won't work when you upgrade Firefox because it deletes essential files needed to reinstate the previous version.

I really like Firefox 4.1, but there are some things from 3.6 that I like better so I did some customizing of 4.1 after I upgraded, and I probably messed up my internet connection when I was customizing. Oh well, I'll probably have to uninstall and reinstall Firefox to fix the problem.

Thank you for your help.  :>)

Update: Just for grins I used my Internet Explorer browser to try and get on the net, and when I did the little dial-up window came up and the 'Connect automatically' option was unticked, so I ticked it, and the Explorer opened up just fine. I then closed Explorer and tried Firefox, and it still wouldn't automatically connect, so maybe if I play around a little more with the dial up connection I can get it fixed. Computers... can't live with 'em, can't live with 'em!

I think in the circumstances and reinstall might be the answer. If there's a corrupt file somewhere, it'll be overwritten when you reinstall FF. These are the steps to take to ensure a clean installation.

Go to Download Firefox 4.0.1 and download a fresh installation file to the desktop.

Then go to Add/Remove Programs, scroll down to Mozilla Firefox and remove it, choosing to keep your bookmarks, customizations etc., (don't checkmark the box).

Then reboot and delete the folder called Mozilla Firefox at this location: C:\Program Files\Mozilla Firefox

Finally run the installation file you downloaded to the desktop earlier.

Your bookmarks, customizations etc., are maintained in a different location and will become available to you again once you complete the installation.

OK, thank you for your help Xircal. I'm going to leave things as they are for now in the hopes that I'll stumble into the solution to my connection problem, and if I don't get it fixed then I'll reinstall Firefox per your instructions.

As an aside, has anybody run into the problem of, when connecting to the net, Firefox will dial the number and get online, but my homepage won't open correctly - I get the 'Connection Was Reset' window, and then when I click 'Try Again' button, my homepage comes up and everything is fine. My Firefox 3.6 exhibited that behavior, and when I installed 4.1 it also did it (until I started having my connection problems).

Me too! I ticked the "NO PROXY" an d nothing will open, but when I tick the ""Auto Detect" they open, but it is so SLOW!! Yeah, I am on dial up. BUT< IE is much faster, and no issues with any site.