So I had the same problem; Actually other problems occurred after upgrade 10.9.2 (Thunderbolt related issues) and now after upgrading to 10.9.4 my internal sound disappeared.
The solutions described above made it worse; Sorry sykosoft .. but your solutions is even dangerous ;
I spend almost a Day finding out how to restore my internal audio devices ..
So what I discovered, this is a software issue;
Update on update on update without any clean install resulted in some filty .plist files
com.apple.audio.DevicesSettings.plist
com.apple.audio.SystemSettings.plist
looking in those files I discovered some settings pointing towards RabbitEars .. perhaps I tried it once in a previous life but now I do believe the upgrade took by incident the wrong 'device' as standard ..
So I looked up and the only thing I could do was finding .kext and other related stuff .. only able to remove it commando wise = terminal
after rebooting for the 722th time performing a SMC and PRAM for the 666th time the result was ... NO STANDARD devices detected 😟 😟 😟
THe only solution working is :
A recovery install;
https://www.apple.com/osx/recovery/
In my case I encountered a problem; My recovery failed (reboot press and hold CMD+R, selecting install fresh OS X)
I find out it was due to my FileVault encrypted HD; So first I uncrypted (switched off FileVault) my HD, and even created a USB recovery disk (not needed)
Tadaaaa 45 minutes later all problems solved, without loosing data or reinstalling all programs ..
*feeling relieved* I thought sharing my pain and solution would save you hours finding out how to repair, hoping PRAM and SMC reset would solve it ..