Jon,
This sounds like a laser pick up type of issue. What makes the most sense is a bad pressing of the blue-ray and DVD in question. The fact that other DVD/Blu-ray disks work on the player tends to eliminate the player as the issue. You stated the region was correct and the disk is undamaged, also that getting a new copy did not resolve the issue. My suspicions are as follows:
* The DVD box says it is for the correct region but the disk is not encoded for the region on the box.
* The polycarbonate material is defective and is filtering the laser light wavelengths and attenuating the signal the pickup is getting to a level that is basically “in the noise” so the device gives up.
My suggestion to find the cause is to try the non-functioning disks in another player or on computer with a DVD drive that is compatible with the disk. (DVD or Blu-ray)
Please note that I have had a computer tell me that the disk is from the wrong region where a set top device just wont play the disk.
One last thing comes to mind.
See if the DVD player has any updates available for it. I had a Sony Blu-ray DVD player awhile back that was very picky on what disks it would play. I found an update setting in the main menu tried it and it resolved the issue.