This is most likely due to either the screw on the back of the home button being too tight/loose. If this is not the cause then it is probably a short in the home button.
The screen sleep magnet could of slipped out of place or energy saver could be set to "never sleep". You could also try to reset the SMC---http://support.apple.com/kb/HT3964.
Personally I would not run the computer with a cable ripped. But then again it is your computer and your choice. I would not risk it unless you still have applecare.
Hi, I had the same problem, and I resolved it today. I had checked the speaker connections but they were all in tact. I ordered a brand new logic board and put it in today. When I turned on my computer the speakers worked great.
