Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem.

• Switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance
• Do NOT click the Reset button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Have tried this and it does not work nor does "Tab Mix Plus." I am finding out that it is Firefox 38.05 that is not working properly.

Went back to the Firefox 37.0.2 everything went back to functioning just as it should i.e. opening new links "Tabs" on websites or in bookmarks. All the extensions, plug-in and excreta also went back to working without any problems.

So going back to Firefox 37.0.2 was the solution / fix until this and other problems with 38.05 are solved

What ways are you trying to open a link in a new tab?

Is that the right-click context menu or isn't a middle-click or holding Ctrl and left-click not working as well?

You may have incompatible extensions if you can't open a link in a new tab.

Did you try to open a new window to see if it works there?

You can create a new profile as a test to check if your current profile is causing the problem.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.

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