Well, getting dasBlog up and running on a shared hosting environment takes a bit of time... and a bit of trial and error. At first I published directly from Visual Studio using the "copy" > "only files needed to run this application" setting enabled, which leaves out (a lot of) files that dasBlog depends upon: trivial stuff like the content folder, things like that.
So, after that I wanted to log in to my ISPs control panel to chmod some of the folders (dasBlog needs write permissions to a couple of folders) only to find out that my password was no longer valid. OK, fine, no worries, I'll wait until Monday for proper human intervention. By the way, this post nicely details all the folder permission dasBlog needs.
Having gone through these steps, I was still greeted by a nice, unhelpful security exception, which told me

Request for the permission of type 'System.Security.Permissions.SecurityPermission, 
mscorlib, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089' failed.

Not very helpful. So, after a bit of Googling I found this post, pointing towards a filelogger for the OpenID activity trace. As is suggested there, I commented out the entire system.diagnostics section from the web.config, since it only deals with this particular trace. After that, the site worked like a charm.