Yes you just have to make sure the jumpers on the drive are set to either "cable select" or "slave" and you have to format the drive with the PC. With that said i would not go diving in with a screw driver just yet... Directv will probably want it back at some point even if a rep or a tech told you the dont want it... That's if its not a owned box of course.
I think the drive is probably SATA and not PATA so it wouldn't need to be set to Cable Select or Slave. If its an external drive - you should be able to hook it up via USB (if the drive you own has USB) or eSATA. If your PC doesn't have eSATA you can buy an eSATA card for your PC relatively cheap from newegg.com or amazon.com
Also - I don't think Directv would want the External drive back as it isn't their property. Unless the OP put the drive inside the HR24 and doesn't have the original drive anymore.
Short answer - YES you can use it on your PC so long as you can connect it to the PC (via USB, eSATA, FireWire etc). You'll need to format it in Windows (or MacOS) and then you'll be good to go.
Edited by LiQiCE, 04 September 2013 - 07:08 PM.