There appears to be two underlying issues with the audio problem. As Apple Support Discussions user "MariusPiatek" explains, one issue is:
Some people lost their audio but they can still hear the start up sound, but no sound afterwards. This is because an update screw up your sound controls probably. Do not worry, this is not a hardware issue as you can hear the sound once you power your mac. A lot of people fixed that issue by playing around with sound settings in the pref Panel.And the other issue is:
No startup sound, no output devices shown. No nothing. Seems like driver does not exist. When you try to turn the volume up, the logo is grayed out and under the volume there is some sort of a STOP icon. Nothing is working when you try to fix this. I was on 10.5.8 and my sound was working perfectly. Then i switched to Snow Leopard and it worked for a few days until i put my Mac to sleep and the next day i realized I had this issue. Upgrading to 10.6.1 did not help ( i am actually not sure if this happened before or after upgrade )Some users have found solutions by resetting PRAM, removing audio preference files, or reinstalling Snow Leopard, though most users continue to see the problem. ASD user "SteveKain" offers this:
I fixed this by going into sounds preferences and selecting Headphones in the sound output device menu. I've got external speakers plugged into the headphones socket and these are automatically detected and listed a headphones. When I unplug the speakers the option in the preferences menu reverts to internal speakers.If you are experiencing these symptoms with your audio, you may want to take your machine to an Apple Authorized AppleCare agent or your local Apple Store to have them diagnose it. Some users report that the problem may be related to poorly seated sound cards. Be sure to have all your important data backed up before taking your Mac in for service.
The other option visible in the sound output device menu is 'Screenflick audio device, and for some reason the system had defaulted to this option automatically, resulting in greyed out audio symbol and no sound. Working fine now.