The 'ATAPI' does make sense, but that is not the brand-name of the burner. You can look in 'nero express' in the first window, the top menu titled "which recorder would you like to use" should have a drop-down arrow/menu and your burner should be listed there. You don't have to post the answer now, just follow the instructions below and post back after.
Those are also the correct file extensions for dvd-video, so that is not the problem.
So here is the steps for copying. First, for testing you will want to save a burn log. Open 'nero express', from the bottom select 'more', then 'configure', then 'misc'. Check the box to "offer to print/save report". Click 'apply' and 'ok'. Do not close the program.
NOW, to copy in nero express, select your burner from the top menu and select 'copy disc' from the second menu. A window opens to choose 'source drive' and 'destination drive'. The 'destination..' should be your burner. The source can be any dvd reader, but use the burner for now, so both windows have the same drive listed. Put the disc to be copied in the drive and select 'burn'. This will copy the disc to your HDD. The drive will open when it is done copying(~10 minutes) and nero will ask for a blank disc. Insert blank and select 'next'. When the burn is finished(~10-15 minutes), nero will ask to save a burn log. click 'yes' and save as a .txt file to your desktop. Then if this burn plays in your other player, report back. If it does not, then report back and attach the log(AFTER removing your name and serial number from the top of the burn log..it is the first 2 lines...just double-click on the file icon on your desktop and it will open in 'Notepad'. Highlight the two lines and right-click and choose 'delete' from the dropdown menu.) to a post using the 'manage attachments' button in the 'go advanced' reply window. We can go from there.