At least I haven't been the only one then!
My solution is running off the main branch from here, and running in IIS Express. Deploying the version was fine, and it was only broken locally.
is that Orchard.Web.1.7.zip ?
My original thoughts were: VS2012 Update 3, or .Net 4.5.1 was the cause.
I have come across the issue twice... I have not closed down the problem to a single thing as I have not been able to reproduce it when I want it.
Both times i had Update 3 of visual studio 2012 installed.
VS 2013 fell the same way after installing vs 2012 and updating to update 3 (I missed 'web essentials', and 'JustCode', and there wasn't any versions for 2013 at the time).
Now I have VS2012 (only) with update 3 installed - no problems so far. I cant remember if I reinstalled windows 8.1 after the broken point (but would have removed any new .net versions).
Im going to reinstall VS2013 again to see if I hit that problem again.
This part of the web.config was added 4 months ago which should ensure that the right version is running:
<assemblyIdentity name="Newtonsoft.Json" publicKeyToken="30ad4fe6b2a6aeed"/>
<bindingRedirect oldVersion="0.0.0.0-22.214.171.124" newVersion="126.96.36.199"/>
Where the problem is im not so sure of now. If it were running in medium trust I would expect to see some permissions errors...
My best answer for now would be to remove the dll from GAC to see if that resolves it. It would have to use the project's file then.