Captain Sim is doing his very best to help me with this problem, but I believe something in the configuration of my FSX installation must be interfering with the fuel cutoff switches.
The only modules I have installed right now is FSUIPC 4.30 and "Walk and Follow".  I removed FSPassengersX because I thought it may be the culprit.
I may try removing W&F and re-install again, or I may just not mess with it right now, since it is not that big of a problem when one considers how really very awesome everything in this 727 simulation is, and fortunately enough, everything else is working perfect.
I went ahead and bought the FS9 version, so if I really want to go through the complete start-up, I can use the FS9 version until we figure out my problem.

I really appreciate all of the help that Captain Sim's support is giving me. ;)  As soon as I discover what is causing the problem, I will let people here know.  I'm sure someone else will run across the problem and need the information.

Thank you,
Bob