Okay, I tried again and again with small small changes to the config and stuff. Finally I found that it is possibly the ASP.NET Development Server that has a problem. But I am not sure. Here is what I did when I got it working:

1. Create an empty database in SQL Server (I use SQL Express on my machine, but NOT the attach-db command. Connecting like to SQL Server).
2. Create a working directory for the website contents - This MUST be a directory that you have NOT used before in the ASP.NET Development Server, since it seems that it caches information about directories, virtual directories and port numbers. It is important to have a CLEAN start on this one, else the error will just pop up again.
3. Copy the .zip contents (the website files) to the working directory and use the release.config as web.config for installation (later for development just switch it for the development.config). Remember of course your specific settings such as connection strings.

Finally it worked for me. I then integrated this website into my solution with parallel development websites with a development and staging website for each DNN version :-)

I ran into this problem today too.  My development machine is running IIS 7, I was able to resolve the issue by switching the trust level to "Full" trust in the web.config.  It seems I can't get DNN running in this environment (including 4.9.x) without making this change. 

This configuration that I use is NOT using IIS, but the ASP.NET Development Server. But like it has been said already, you need a virtual directory for each DNN installation/version.

The ASP.NET Development Server enables you to define your own Virtual Directory name and port. So you simply make sure that your ports for each DNN Version on the server are different and remember to do the same with the Virtual Directory names. Like I mentioned earlier, my Database-name and Virtual Directory correspond more or less to the name of the version. E.g. 05.00.00_Staging.... This is by default my physical directory name, my virtual directory name, and using a suffix also the main part of my DB name (eg. DNN_05.00.00_Staging).

You may even adjust your hosts-file and provide an alias for your portal like http://05.00.00/ and then remember to register that alias in your installation of course. This way you avoid having to go to eg. http://localhost:1234/05.00.00/

This environment works like a charm for me and I haven't found a problem with it (yet).