This is a Windows Forms group. The OP needs info on winforms threading
methinks.

Bob

Do you have any examples of using BeginInvoke?  

I've tried creating a new thread off of the main UI thread (which opens the
new form), and in this new thread, processesing my progress bar.  I'm getting
two behaviors that are strange.  #1, if I use a timer to process the progress
bar, nothing happens at all.  #2, if I create my own looping structure to
process the progress bar, it works, but when the new form is opened, I lose
all context and the ability to view the progress bar.. which is the original
challenge.

I have to disagree with you here.
You could have multiple UI thread. The anciliary one being run with a
ShowDialog() (instead of Application.Run()), as it is described in all
splash screen samples.
Even those from MSDN.

InvokeRequired is also inappropriate at startup time, where Aplication.Run()
has not even been called yet!

you could use a splash form even before Application.Run() ;-)

=== Warining: pseudo code below ==========
public class SplashForm : Form
{
   Thread localUiThread;
   public void ShowSplash()
   {
       if(localUiThread != null)
           return;
       localUiThread = new Thread(delegate() { ShowDialog(); });
       localUiThread.Start();
   }
   public void HideSplash()
   {
       if(localUiThread == null)
           return;
       BeginInvoke(new MethodInvoker(delegate() { ThreadStop(); }));
   }
   void ThreadStop()
   {
       if(IsDisposed)
           return;
       Close();
   }
}