onorio56, since you say this is just a one-time thing to rescue a few videos before you turn in the box, your best bet is to just make a real-time dub onto any recording device you can lay hands on: even an old VCR will work, if you don't need HDTV quality and just want to catch up on a few shows.
You connect the analog video (yellow) and audio (red/white) line outputs in back of the PVR to the inputs of a DVD recorder or a VCR. Connect the line outputs of the "saving" recorder to one of the inputs of your TV, and set the TV to show that input. Turn on the DVD recorder or VCR, set it to the input you plugged the Pace into, and you should be able to view the Pace box video patched thru the other recorder on your TV. Hit "record" on the DVD recorder or VCR, and play whatever shows you need to save on the Pace box. If the show runs an hour, it will take an hour to copy, etc, and you will need to pay attention to how much time you have left on each DVD or videocassette.
Depending on the channel the Pace was recording, some shows may be copy-protected, meaning a DVD recorder will shut itself off and refuse to copy those particular shows. To get around this would require buying a video protection filter or TBC, which again is not practical just to save a few videos (filters cost $100-200). If you discover the Pace videos are protected, just use a VCR instead of a DVD recorder: the VCR technology is "dumb" and doesn't respond to the Pace "do not record" signal.
Quite honestly, the whole task is really not worth the trouble of bothering and you may be overthinking this: it takes as much time to make the copies as it does to *just watch the shows*. If the Pace is functioning normally enough to let you play the recordings you want to catch up with, how about you simply don't trade it in until you watch the backed up recordings? Take a day off, or put off other things until you can force yourself to watch everything. Then trade in for a new box. Or, get the new box as an additional monthly charge and hold onto the old one until you finish watching everything on it: even if it takes you two months, what could it cost? another $30 in box fees before you turn it in? Much easier and cheaper than futzing around trying to get videos off the old box first.
BTW: lately, AVS has been getting a number of somewhat suspicious questions similar to this, with people harping on the "laptop" idea. The thing is, no one in their right mind tries moving videos from a decoder box PVR to their laptop unless A) they literally have no other device in the house capable of recording video and hope to avoid buying another recorder, or B) they're playing "dumb" hoping someone here will reveal some "secret" trick to copy digital files from a decoder box to a laptop (because they want to use the laptop as a portable viewer, or they want to upload cable videos to internet sites). I'm not saying this is you, onorio56, just pointing out that cable/satellite companies are aware of these desires and very actively discourage/prevent the possibility.
So there really isn't a "cheap and easy" (i.e. do it in minutes via digital file transfer) way to get videos off a cable/sat PVR and into a PC/laptop. You can dub the videos from PVR to a DVD recorder, then put the DVDs in your laptop and rip the DVD files into AVI, MP4 or DiVX format (for standard-def copies). Or, you can lay out the money for something like the Hauppage, which lets you connect the output of the PVR directly into your PC to capture full HDTV-quality AVCHD files. Either way, it won't be fast: a one hour show will take one hour to copy. It won't be direct digital. And you might have to spend another $100-200 on a video filter. Alternatively, as Kelson suggested, when you turn in your defective Pace box don't replace it: buy a TiVO instead. The TiVO lets you transfer recordings as digital files directly to your PC via ethernet connection: by far the easiest system if you expect video archiving to be an ongoing hobby.
Dealing with all this hardware, expense, time and aggravation is worth it if you intend to make a steady hobby of capturing TV to your computer, but the whole enterprise is a little ridiculous if all you need to do is catch up on some backed up shows before turning in a faulty box.