On the diagnostic page of MACH 3 you can see the status of all the pins on the parallel port. If you ground some of the input pins you should be able to see the status change, if your port is talking to the software. Integrated video card should make no difference.
It's possible that the physical parallel socket you're using is not set up in windows to the default address that Mach3 is expecting. Read the Mach 3 manual and you'll see how to look up the address in the Windows device manager and set it in the Mach 3 parameters. If you have several ports in the device manager, you could try each address in turn in the Mach 3 parameters until one of them resonds to the input test described above.