Did you installed ASK toolbar?

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).

To Enable SafeMode

• You can open Firefox 4.0+ in Safe Mode by holding the Shift key when you open the Firefox desktop or Start menu shortcut.
• Or open the Help menu and click on the Restart with Add-ons Disabled... menu item while Firefox is running.
• Once you get the pop-up, just select "'Start in Safe Mode"

If it works in Safe Mode and in normal mode with all extensions (Tools > Add-ons > Extensions) disabled then try to find which extension is causing it by enabling one extension at a time until the problem reappears.

Close and restart Firefox after each change via "Firefox > Exit" (Windows: Firefox/File > Exit; Mac: "Firefox > Quit Firefox"; Linux: "Firefox/File > Quit")

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode
• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

I tried safe mode and also I reset firefox to default and it still does not work correctly. These same links will open new tabs in explorer, so it not that they are controlling this

Create a new profile as a test to check if your current profile is causing the problems. 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

Profile Backup and Restore

• http://kb.mozillazine.org/Profile_backup
• https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

Mouse to the link, right click and look at the choices, Among them should be; Open New Tab and Open New Window. When you left click a link on the current page, that link is opened in the current window be default.

Right click has always worked on links. I discovered that the problem is only if I am using yahoo as my home page. If I use google/ig as a home page the links work correctly. So for some reason yahoo is the problem

The setting in Firefox/Tools > Options > Tabs: "New pages should be opened in": "a new tab/window" is for links that specify a target window to open the link.
That option allows to divert such links to a new tab instead of a new window.
Links that do not specify a target open in the current tab unless JavaScript changes this.
If that isn't the case then you may have an extension interfering.
For links that do not specify a target use a middle-click or hold down Ctrl and left-click the link or use the right-click context menu to open the link in a new tab or window.
This applies to bookmarks and other links as well, i.e. you can middle-click the View Image item in the right-click context menu of an image or middle-click the Reload button on the location bar to get a new tab with that link.
Left-click a JavaScript link to avoid getting a blank tab.