It sounds like you have a third party program that has taken over your search engine, home page, and/or the default new tab page. Fortunately, this can be remedied easily:

1. At the top of the Firefox window, click on the Firefox button (Tools menu in Windows XP), and then click Add-ons. The Add-ons Manager tab will open.
2. In the Add-ons Manager tab, select the Extensions panel.
3. Select the toolbar you wish to remove.
4. Click the remove button.
5. Click "Restart now" if it pops up. Your tabs will be saved and restored after the restart.

After Firefox restarts, install the Search Reset Tool. This will remove the rest of the traces of this program from your Firefox.

For further information, please read Remove a toolbar that has taken over your Firefox search or home page.

Did this fix the problem? Please let us know!

Some security software has a feature to protect you from unwanted browser changes. However, this also can prevent you from making changes you want to make. If you have Advanced SystemCare, or if any of your security/utility software has a feature with a name like Browser Protection, Home Page Protection, or Surfing Protection, try turning off that feature.

By the way, how often does Firefox crash? When Firefox crashes, it usually records information about what was happening at that moment. You can submit that data to Mozilla and share it with forum volunteers to see whether it points to the solution. Please check the support article "Firefox Crashes" (especially the last section) for steps to get those crash IDs, and then post some of the recent ones here.