In DVD Player, if you select "Get Disk Info" from the menu, and click on the "Region" tab, it will tell you both the disc and drive region up at the top (above the map--the text is easy to miss), as well as how many region changes your drive has left (down at the bottom).
But it would be obvious if the problem were a region issue as soon as you stuck the drive into the computer--if it wasn't the same region as your drive, you'd be informed of this and asked if you wanted to change the drive region.