(How) can I block a specific program in Windows 7 from checking for other instances of the same program running within the local area network?

I want to run two instances of the same program on two PCs of the same home LAN in Windows 7.
If one instance of it is running on one of the two PCs, when I try to run another instance on the other PC, I get the following error message:
“Another instance of this program is running on another network computer using the same serial number”
The only option is OK and the program closes.
I’ve blocked all 3 .exe files I found in its installation folder, using Windows firewall (both outbound and inbound), to no avail. I get the same error message.
I’ve run Process Explorer, the only process there is when I run it is just its .exe file to launch the program.
The only other thing I can think of is trying to find what port it uses to perform this network check and block it.
I’m not that good in this, so I need some hints/guidance.
Thank you.