Your GridView's datasource is a List of string (containing the path of your folders).
Your bound hyperlink contains an Eval instruction asking to retrieve le FullName property of every item of your DataSource. Your DataSource being a List, it could be translated like that :
foreach(string path in files)
{
HyperLink1.NavigateUrl = path.FullName;
}
Now hopefully you're beginning to see the problem : the string class doesn't have any FullName property.
The solution is to replace the Eval (which is a bad solution anyway, since it does reflection and isn't very efficient) by :
<%# Container.DataItem %>
Which is a typed variable even that you can cast
so you could even write this :
<%# (string)Container.DataItem %>
EDIT : sorry, I wrote code in C#, I hope you'll understand (and that my solution works in VB !)