"Gave up waiting for root device" while booting
Solution 1:
I'm experiencing something similar after upgrading from 13.04 to 13.10. I haven't solved it but can get it to boot by doing the following.
From the initframs prompt try typing "ls /dev/mapper" and see if your root volume is listed. If it is not listed, try waiting 10 seconds and run ls again.
If it is now listed, type "exit" and it should now find the root device and boot.