I can't take responsibility for this as I googled it and the answer was by James Newton-King found here- How to present credentials in order to open file?
You want to impersonate a user who does have the rights to access the file.
I recommend using a class like this - http://www.codeproject.com/KB/cs/zetaimpersonator.aspx. It hides all the nasty implementation of doing impersonation.
using (new Impersonator("myUsername", "myDomainname", "myPassword"))
{
string fileText = File.ReadAllText("c:\test.txt");
Console.WriteLine(fileText);
}