You need to scan your computer for virus/spyware infections. Although, you may be having a problem with some extension or plugin that is hindering your Firefox's normal behavior. Have you tried disabling all add-ons (just to check), to see if Firefox goes back to normal?
Also, and just in case, here's how to change your homepage:
Do a malware check with a few malware scan programs.
You need to use all programs because each detects different malware.
Make sure that you update each program to get the latest version of the database.