I was correct all along. It was the registry. Here's what went wrong and how I solved it:
* Upon installation, the ATC Voicepack SDK from Microsoft altered certain values in the registry pertaining to MSXML 4.0. It also added (or copied) two MSXML files to System32. The reason for these changes remains unknown. Ditto regarding its mechanism. Such a scenario is probably extremely rare.
* The above was the reason why BGLComp believed that the MSXML 4.0 installation was either non-existent or faulty, thus producing an identical error in all programs that use bglcomp.exe -- ADE, ExcBuilder and Rwy12.
* The situation with the registry was such that un-installing MSXML 4.0 was not changing anything inside the SysWOW64 folder or properly changing things in the registry, even though add-remove showed that the program had been "un-installed" (i.e. the entry in add-remove goes away). The opposite (i.e. installation) produced the same results.
* With your helpful posting of screenshots of the contents of your System32 and SysWOW64 folders, I was able to determine what should actually be inside those folders vis-a-vis MSXML 4.0.
* Things looked exactly like yours after I deleted the mysteriously added files in System32. However, nothing was working because the un-installs/re-installs were not changing anything inside SysWOW64.
* Although everything seemed normal (albeit MSXML 4.0 not allowing BGLComp to compile), I decided that the problem must be the registry, so I fired up every program that used MSXML 4.0 until I found one that malfunctioned. That malfunction said that "MSXML 4.0 was not properly installed".
* I went for broke and screwed up the registry on purpose by physically removing msxml4.dll and msxml4r.dll from the SysWOW64 folder without unregistering them and placed them on the desktop.
* I ran Uniblue's RegistryBooster in order to find the errors I had just created by taking the step above. It found 17 system errors that it did not pick up before. All of the errors involved MSXML 4.0. I had the program fix those errors and rebooted.
* After the computer rebooted, I went to Command Prompt and unregistered the two DLLs that now resided on my desktop. After that, I threw them out.
* I rebooted again and reinstalled MSXML 4.0 SP3 (the one without the SDK; it's not needed) and the SP3 KB update.
* This time, the install did make changes to the SysWOW64 folder (i.e. the files were placed there) and correctly wrote to the registry.
* I fired up the program that had earlier told me that "MSXML 4.0 was not properly installed" and it did not pop up that message again. The program worked perfectly.
* I went to ADE and it's now compiling. Ditto regarding ExcBuilder and Rwy12. BGLComp.exe is also working if I drag an XML file on top of it.
Thank you all for your help. It provided considerable assistance in guiding my train of thought. Cheers all.