@acer and @tomleslie  All very helpful!  Executing the garbled file in Maple 2020.1 works for me, too, as you might expect.  All looks great after the execution step.  Thanks!

P.S. Can Maple correct the Java errors that @acer found leading to errors in the 2D plot color shader and interpretation?

@tomleslie Curious, indeed.  Your "Download workingNow.mw" file works fine for me, too, with Maple 2020.  But my original Model050913.mw shows a garbled display with Maple 2020 on my computer, as seen in this screenshot:

The display is garbled with Maple 2020, as the screenshot shows, whether I open my problematic file from the MaplePrimes link or open the original file on my computer.

Based on your success, I loaded Maple 2020 onto a different computer.  But the result is the same garbled and unusable display as shown in the screenshot above. 

Your success with Maple 2020 and my failure with Maple 2020 on two different computers with 2 very different graphics systems is curious.  In any case, I am using Maple 18 to interpret and re-save the garbled .mw files for use with Maple 2020.  Perhaps our experience might help other Maple users with .mw files from the early 2000s, if they encounter garbled files with recent versions of Maple.  Thanks for your help!

A problematic worksheet now is attached to original post and here:

Model050913.mw

The solution to this problem is to install Maple 2019.1 (32-bit) into the default installation directory "C:\Program Files (x86)\Maple 2019".  I had been installing into the directory "C:\Program Files (x86)\Maple". 

Installing 32-bit Maple versions into "C:\Program Files (x86)\Maple" produced a working Maple add-in with Excel up through Maple 2017.3.  Installing Maple 2019.1 (32-bit) into "C:\Program Files (x86)\Maple", however, led to a non-functioing Maple add-in with Excel 2016 (32-bit).

In summary, installing Maple 2019.1 (32-bit) into the default installation directory "C:\Program Files (x86)\Maple 2019" solved this problem with the Maple add-in to Excel. 

@tomleslie Your report is helpful.  Your report encouraged me to test Maple 19.1 (32-bit) with Excel 2016 (32-bit) after I deleted the 64-bit version of Maple 19.1 from my computer.  The Maple add-in to Excel still produced the error message "The specified module could not be found.  OpenMaple cannot find Maple engine library, maple.dll."

After I reinstalled Maple 19.1 (64-bit) and Maple 17.3 (32-bit) to my computer, the 32-bit Maple add-in to Excel worked fine based on pairing Maple 17.3 (32-bit) with Excel 2016 (32-bit). 

This experiment combined with your experience with the 64-bit Maple add-in for 64-bt Excel suggests that an attempt to work with Maple 19.1 (32-bit) with Excel 2016 (32-bit) is problematic.  In other words, the 32-bit enviroment for the Maple add-in might be a problem for Maple 19.1 (32-bit).

I tested the 64-bit environment for the Maple add-in on a different computer.  The Maple add-in for Excel 2016 (64-bit) worked fine with Maple 19.1 (64-bit) on this different computer that is running Excel 2016 (64-bit).  This result suggests that the Maple add-in for Excel works well in a 64-bit environment for Maple 19.1.  The combination of your findings and my findings point to the 32-bit environment of Excel and Maple 19.1 as the origin of the problem that my computer is experiencing with the Maple add-in for Excel 2016 (32-bit) and Maple 19.1 (32-bit).  

Here is additional information from my testing:

The Maple add-in for Excel works fine with Maple 2017.1 (32-bit) and Maple 2017.3 (32-bit) on my computer that has Excel 2016 (32-bit) and Windows 7 (64-bit).  In contrast, the Maple add-in for Excel does not work with Maple 2018.1 (32-bit) or with Maple 2019.1 (32-bit) on my computer.

Maple 2019.1 (64-bit) works fine on my computer, although I do not use Maple 2019.1 (64-bit) with Excel.

I obtained these results by sequentially installing various versions of Maple:
Maple 2019.1 (32-bit)—Maple add-in for Excel add-in does not work despite repeated reinstallations and uninstallations
Maple 2017.1 (32-bit)—Maple add-in for Excel add-in works
Maple 2017.3 (32-bit)—Maple add-in for Excel add-in works
Maple 2018.2 (32-bit)—Maple add-in for Excel add-in does not work
Maple 2017.1 (32-bit)—Maple add-in for Excel add-in works
Maple 2017.3 (32-bit)—Maple add-in for Excel add-in works

Plausible conclusion:  Something is wrong with the way Maple 2018 (32-bit) and Maple 2019 (32-bit) work with Maple add-in for Excel 2016 (32-bit).

What is different about the way Maple 2018 (32-bit) and Maple 2019 (32-bit)  work with the Maple add-in for Excel compared to Maple 2017, at least in a Windows 7 environment? 

Why does Maple 2017 work fine with the Maple add-in for Excel, but Maple 2018 and Maple 2019 do not work with the Maple add-in for Excel?

What is the fix for Maple 2018 and Maple 2019 for the Maple add-in to Excel?

The Windows registry entry at Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\excel.exe\Path is not important for the Maple add-in to Excel, at least for Maple 2017.  The Maple add-in from Maple 2017 works fine without changing this registry entry.