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

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.com/kb/Safe+Mode

If it does work in Safe-mode then disable all 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 you can use one of these to start in Safe mode:

• Help > Restart with Add-ons Disabled
• Hold down the Shift key while double clicking the Firefox desktop shortcut (Windows)

• https://support.mozilla.com/kb/Troubleshooting+extensions+and+themes

Restarted in safe mode using Help>Restart with all addons disabled.

No Change.

Still no tab close buttons on the tabs. Only a CNTRL-W or a right click on the tab and selecting close tab will close the active tab.

You can check if the close buttons are still enabled.

• http://kb.mozillazine.org/browser.tabs.closeButtons

To open the about:config page, type about:config in the location (address) bar and press the "Enter" key, just like you type the url of a website to open a website.
If you see a warning then you can confirm that you want to access that page.
You can use the Filter bar at to top of the about:config page to locate a pref more easily.

Thank you very much for your help. That was it the tab close integer value was set to 33 for some unknown reason. I reset it to an integer value of '1' and that solved the problem.

Thank you again.

You're welcome.

Maybe you may have tried to changed it once to 3 (only a close button at the far right end) and typed two '33' instead of one '3' ?