The HDMI digital output of the DVR has DRM on it to prevent you from connecting it to a PC, but if your PC has analog video input, you can take an analog video output from the DVR and then view it on the PC, but that's a rare configuration for PCs. Some HPs had analog video cards from the factory, otherwise you'd need to add a card.
---FIOS---DVR===analog video & audio===PC/video interface
There are audio+video to/from CAT5 adapters on the market you can use to transform the signal so it can be sent to other floors. That would require CAT5 floor-to-floor, since the signal the balun outputs is not Ethernet, so I would STRONGLY suggest using plenum rated cable if you haul it through ductwork.
You could also get a TV tuner for http://www.mythbuntu.org/ and watch+record over-the-air TV.