File -> New Window or Ctrl+N.

Fox Splitter (formerly Split Browser): https://addons.mozilla.org/firefox/addon/4287

As far as I can see all this does is open a new window and cover up all old windows. I want two windows open simultaneously.

My problem is that Ctrl+N is not working... and it happened suddenly, like it's due to a recent update. The same thing is happening on both home PCs and it's very frustrating. In fact I'm using MSIE right now because of it.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of your add-ons is causing your problem (switch to the DEFAULT theme: Tools > Add-ons > Themes).

See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems and Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems

Yes, I checked all add-ons and extensions one by one immediately after posting, but not in safe mode. Turns out there were different issues on the two PCs. An EndNote plugin was the problem on one PC, which really surprised me. The other PC had a combination of Microsoft .NET and Adobe DLM (which is apparently no longer even available on Mozilla). I'm able to open new pages now, what a relief!