More joys getting Sitecore to run on my machine. For some reason the App Pool of the Sitecore instance was set to .Net 2 rather than .Net 4. This required going into IIS Manager and changing the App Pool setting.
Sitecore had also managed to set the database connection string to my local user rather than a builtin account. I had to edit the username and password in AppConfig/ConnectionStrings.config in Visual Studio and rebuild the solution in order to make it work.
I wish Sitecore would use HTML documentation rather than PDF – it makes jumping to the right spot in Google searches very difficult.