For this question I only care about the specific instance. In other words, I do not care about any other threads that using Excel.

Ideally my vba functions should not do anything when running under any web browser. But, everyone here uses IE 6 or IE 7, so that might simplify things.

Something like this pseudo code:

if ThisWorkbook is RunningUnderAnyBrowser then exit function.

Check the ThisWorkbook.Container.Name - if Excel is running normally, this will cause an error; if under IE, it should return "Microsoft Internet Explorer" (or something similar) ar it will return the name of the container application if the workbook is embedded in say a Word document. I have a recollection that you can't use this directly in the Workbook_Open event - you need to use Application.Ontime with say a 1 second delay.
HTH
Rory

That worked great.  But, FYI,  I was wrong about using Thisworkbook.
Here is what I had to do instead.  
    on error resume next
    For Each Workbook In Application.Workbooks
       x = Workbook.Container.Name
        If Not IsEmpty(x) Then GoTo exitsub
    Next Workbook
Thanks a ton

Glad it worked!
Rory.

related questions are Q_22130186 Q_22130644 and  Q_22129061

and, for an even more complete solution, see
https://www.experts-exchange.com/questions/23847763/How-to-tell-if-Excel-is-running-under-ie6-or-ie7.html?anchorAnswerId=22805912#a22805912