Thinking out loud...

I would consider the following.
Create a little monitoring application that you can register as a windows service.
Then with your webapp via IPC or named pipes or something similar register itself using a unique token for that webapp and ask if it is the first with that token.
This can be extended with things like start time etc..

To be fair.. I would not write the monitoring app in DataFlex.
The reason for that is that DataFlex does not have any existing logic for the windows API ( )
So it will be harder and needs extra "run it as a service" tool, plus you might get extra license counting issues and what not. Aka.. just not the tool for that particular job.