Here is a short and simple question with a simple answer.
Question: How can I determine the Revit product's serial number?
Answer: The Revit serial number is available in the Licpath.lic file, which is a text file located in the Revit program folder. The content of the file is something similar to the following, where the string after # SN is the serial number:
## Autodesk Revit ## License Information # SN 123-45678910 # NSN 000-00000000 # Standalone