Maybe something like this (uncompiled, untested):

    UserData dataFileShare, dataAD, data;
    Thread threadFileShare, threadAD;

    threadFileShare = new Thread(new ThreadStart(delegate()  
{ dataFileShare = GetFromFileShare(userName); }));
    threadAD = new Thread(new ThreadStart(delegate() { dataAD =  
GetFromAD(userName); }));

    threadFileShare.Start();
    threadAD.Start();

    threadFileShare.Join();

    if (dataFileShare != null)
    {
        data = dataFileShare;
    }
    else
    {
        threadAD.Join();
        if (dataAD == null)
        {
            throw new UserDataNotFoundException();
        }
        data = dataAD;
    }

Note that I'm still getting used to the anonymous delegate syntax and rely  
on the compiler to tell me what exactly I need to do.  The above might not  
compile right off the bat, but if not hopefully the compiler error will  
give you good direction.  I think the basic idea is correct.

Pete