I understand for your comment that the installation is already finish and the exceptions appear after the install is already complete?. You can run your site the first time?
all the errors in your log are security exceptions more specific FileIOPermission, this is caused because a app is trying to read or write in a file with out the right access permission.
Are you sure that you have all the permissions on the /App_Data and /Data folder and all sub folders and files inside it are writable by the web process user (the user that is the identity on your application pool in IIS Web Server), and that the permissions wasn't changed, after the install.