Unfortunatly the particular box you have, a Motorola DCT6416, is locked down pretty tight by the cable companies so you have only two options open to you to transfer your recordings:
1. Get a VIVO or TV tuner card, connect the composite or S-Video (S-video is preferred due to better video quality) outputs to your capture card, and using the software that came with your card capture the video real-time.
2. You can use the firewire port on the back of your box to try and transfer the recordings. You can find the steps to do this here:
http://replayguide.sourceforge.net/dct6412/
The easier of the two would be to use a capture card since some recordings may be encrypted in such a way that they'll prevent you from transferring via firewire. It's the method my husband and I use with great success, using an ATI TV Wonder 650, and the only challenge we found was finding a software suite to edit the video. We wound up using a combination of Adobe Premier Pro 2 and Easy Media Creator 10 to get the best overlap of tools.
Also, just as a side note, in regards to the eSATA port on the back of your box they've probably been disabled. When we tried to use an external drive Comcast advised us that they were locked out from being used but, hey, you may get lucky just make sure that the eSATA drive you get you'll be able to use for something else if it does not work.
Hope this helps!