If you have the Motorola DCH3416, you should buy a FireWire cable (also known as a IEEE1394 cable) to connect from your PC or Mac to your cable box.
One thing we don't know is if your computer has FireWire currently. You should post a picture of the outputs so that I can identify them. If you do have FireWire, you need to determine the type and size of the the FireWire connector on your machine. Laptops typically have either the 4-pin IEEE1394a connector or the IEEE1394b connector. Your cable box has the 6-pin IEEE1394a connector (all Motorola cable boxes have the IEEE1394a connector.)
It's likely that you'll need a "4-pin IEEE1394a to 6-pin IEEE1394a" cable, but we'll determine that when you get back to use with more info. It is also very possible that you have no FireWire on your computer at all, in which case you'll need to buy a FireWire card.
Once you get squared away on the FireWire stuff, you'll want to download my Windows Installer .MSI installation package which simply bundles together the needed drivers and software to capture HDTV. You can download it from here
, but it only works on 32-bit editions of Windows XP, Vista, Windows 7 and Windows 8; The drivers can not work on 64-bit Windows (64-bit drivers don't exist for capturing HDTV and nobody is working on creating any.) This installation includes a freeware software product "CapDVHS", which allows you to capture HDTV. It's pretty easy to work with and my install includes some documentation.
If you use a Mac, you simply need to download and install the Apple FireWire SDK, which includes an app that captures HDTV.