I actually managed to fix this one on my machine! I looked in the logs (at C:\Users\Leon\AppData\Local\dftmp\DevFCLogs) and noticed that the Compute Emulator (or some related process) tries to create an endpoint on TCP port 120001:
On my machine this port was already taken by the 'VMWare Workstation Server' Windows Service (vmware-hostd.exe), which comes as part of VMWare Workstation 8.
I stopped the VMWare Service using the Services Management Console and then I was able to start the Compute Emulator without any problems!
To initialize storage
Click Start, point to All Programs, and then click Windows Azure SDK v1.3.
Right-click Windows Azure SDK Command Prompt, and then click Run as administrator.
In the Windows Azure SDK Command Prompt window, type the following command:
other
DSInit /sqlInstance:<SQLServerInstance>
Where <SQLServerInstance> is the name of the SQL Server instance.
You can also use the following command, which uses the default instance:
other
DSInit /sqlInstance:.
Or, you can use the following command, which reinitializes the database:
other
DSInit /forceCreate