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).

• Don't make any changes on the Safe mode start window.

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

If it does work in Safe-mode then disable all your extensions and then try to find which is causing it by enabling one at a time until the problem reappears.

• Use "Disable all add-ons" on the Safe mode start window to disable all extensions.
• Close and restart Firefox after each change via "File > Exit" (Mac: "Firefox > Quit"; Linux: "File > Quit")

>In Firefox 4 Safe mode also disables plugins (Tools > Add-ons > Plugins) and hardware acceleration (Tools > Options > Advanced > General)

The root of the problem is Speed Dial extension. I don't know why do they reassign Ctrl-Number shortcut by default (implicit change of any settings seems to be a bad habit). I've changed this extension's Keyboard Control "Ctrl-<number>" settings (4th tab) back to "Select Tab" and everything fell into place at once.

P.S. MiniWeather.com link is just the first button in the Speed Dial's list. Those who have more links may encounter similar problems with Ctrl-2, Ctrl-3, etc. as well.