Try the Firefox SafeMode.
A troubleshooting mode, which disables most Add-ons.
(If you're not using it, switch to the Default Theme.)

1. You can open the Firefox 4/5/6/7 SafeMode by holding the Shft key when you use the Firefox desktop or Start menu shortcut.
2. Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.
   

To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut (without the Shft key) to open it again.

If it is good in the Firefox SafeMode, your problem is probably caused by an extension, and you need to figure out which one.
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes

Sorry for asking but I presume your mouse is working with IE and your mail program. Lists of add-ons are in Help>Troubleshooting Information.

But first work through the-edmeister's answer.

No good.

Yes. I did everything you asked.

I don't see how you could follow the-edmeister's instructions without a left click? Does it work occasionally?

It is not clear from your answer whether you actually tried Internet Explorer. It is difficult with left click not working but go to your IE Desktop icon and right click on it, then try to left click on Open and see if you can get that started.

I also presume you've looked through the "Mouse" entry in the Control Panel. Mine says my mouse is working correctly. Do you have an old mouse or can you borrow one? I think there is a strong chance you have a mouse problem not a Firefox problem.

My mouse works perfectly everywhere except in Firefox 5 and it is a relatively new Microsoft USB optical mouse. The left button does not work anywhere in Firefox 5.

Reconfigure your Mouse Options from Control Panel -> Mouse After you are Done, click OK

Check and tell if its working.

There is no way to reconfigure my mouse options from the control panel.

Open Control Panel -> click Mouse -> Buttons section -> Remove Checkmarks from Switch Primary and Secondary buttons and Turn ON ClickLock

-> Pointers section -> select Windows Default (system scheme) -> Remove Checkmark from Enable Pointer Shadow

-> Pointer Options -> select a Pointer Speed -> place Checkmark on Enhance Pointer Precision -> Remove Checkmarks from Automatically move pointer to the default button in a dialogue box , Display pointer trails , Hide Pointer while typing , Show location of pointer when i press the CTRL key

-> Wheel section -> Roll the wheel one notch to scroll: select The following number of lines at a time -> choose a number e.g. 3,4,5 etc.

-> click OK

Check and tell if its working.

I think you are on the wrong path here. There is nothing wrong with my mouse settings. The mouse works perfectly everywhere except inside Firefox 5.

Try this:

-> Tap ALT key or press F10 to show the Menu Bar

-> go to Tools Menu -> Options -> Advanced -> Remove Checkmark from Use Hardware Acceleration -> click OK

Check and tell if its working.

Still no left click function within Firefox 5.

Create a new profile as a test to check if your current profile is causing the problems.
See Basic Troubleshooting: Make a new profile:

• https://support.mozilla.com/kb/Basic+Troubleshooting#w_8-make-a-new-profile

There may be extensions and plugins installed by default in a new profile, so check that in "Tools > Add-ons > Extensions & Plugins" in case there are still problems.

If that new profile works then you can transfer some files from the old profile to that new profile (be careful not to copy corrupted files)

See:

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

Try hitting the F7 key to TURN OFF Caret Browsing

http://kb.mozillazine.org/Accessibility.browsewithcaret

Check and tell if its working.