Well, finally success and the last poster was right in the ballpark. My issue was that something in my system (probably the registry) was unable to display the proper shortcut arrow on my desktop icons. Where it got the graphic that was displayed was beyond me since my in place upgrade wasn't a Vista to Win 7 but XP pro to Win 7 using Laplink PC Mover.
The solution was the Vista Shortcut Manager which you can get if you google it. While designed for Vista, it worked like a charm in Win 7. One of the options is to not display the shortcut arrow and this option fixed my desktop. TweakUI was the XP tool for doing this.
So, anyone with a similar issue should try the Vista Manager and you should have the same results as me. I'm a very happy camper and I want to thank all of you who took the time to help me with your suggestions.