Soft keys are not working

I would suggest you go into Settings, About phone, and tap Build Number until it tells you "You are a developer." Back out and now you have Developer Options above About phone. Enter that, and look for the Input section. Enable Show touches and Pointer location. Now touch on your screen, and "draw" down to the soft home keys.

Does the screen indicate registering your screen touches over that area? If it does, then the screen is working, and there must be something else wrong. Depending upon your ROM and version, you might need to factory reset your phone, or flash a factory image from Google.

Disable Developer options before pursuing other avenues.