I recently (for reasons not worth rehearsing here) disabled and uninstalled the audio drivers on my E6410. When I reinstalled using the IDT driver from the Dell website, I found that only my headphone output was working properly. The speakers do work but are quiet, tinny, and highly distorted.
I've tried re-installing the IDT drivers, and I've tried uninstalling them to force windows 7 generic drivers, but the problem remains. I stress that i do get speaker sound -- it is not wholly inactivated so it seems unlikely to be a problem with the headphone jack
Try running the Dell Diagnostics audio tests. If the audio is just as bad during the tests then it is a hardware failure.