I recently installed a test environment on my Windows 7 laptop [using New-SPConfigurationDatabase] but I was unable to add a new Web Application. I created a new user, added it to the Local Administrators group.
Two issues were apparent:
A. I could not add a new Farm Administrator as 'I needed Local Administrator rights' [from the ULS]
B. I could not create a new Web Application [due to security trimming]
The solution lies in the OOTB Administrator account that is provisioned in the Windows 7 installation; it is deactivated by default.
I activated the account and, presto, used its credentials to perform all the required activities.