|USB (1.x and 2.0 rated ) ports are able to supply up to 500ma of current (1/2 amp) per USB port, under the best circumstances. USB ports built into computer mboards can usually supply that - that may not be the case for the USB port(s) on the DVD player. |
3.5" hard drives require a lot more than 500ma of current, in total, and they require that at both +5v and +12v - USB ports are +5v only.
You could buy a external enclosure for the hard drive, then install the hard drive in it - the enclosure comes with an external power adapter if it's for a 3.5" hard drive. If the USB port on the DVD player can supply 500ma of current, then the hard drive should work fine with it.
USB flash drives, on the other hand, require a much smaller amount of current, usually well under 100ma.
Whether the DVD player can recognize movie (or audio or picture) files on the drive depends on the capabilities of the DVD player.
E.g. I have a standalone Samsung DVD player that can only recognize files on USB connected drives that have certain file extensions.