Yes - %PATH% settings was my first thought, also. Are you specifying a location for the exe in your code at all, or relying on Windows to find it?

Easy enough test - drop into a random directory (which does NOT hold the ffmpeg.exe) on both PCs, and try running the exe from that path - I suspect you'll find it'll run on one but not the other. If that's the case, the below link has some pretty pictures to go along with tis write-up on how to add/modify entries to your path... in the first instance, I'd follow it on both PCs to the point where you can see the PATH and compare the two, and modify where appropriate.

Note - as with modifying the registry, modifying the PATH settings CAN be detrimental (not as much as playing with the registry can be, but still worthy of caution) to the performance of your Windows install. A good pinch of caution is always advisable.