Cable Signal Testers

Since they went to the trouble to wire a pair of CAT-5 cables at each receptacle, they likely wired them all back to a central patch panel in a closet or wall cabinet that looks something like this:

If that's the case, then none of the outlets are "live" and would need to be patched over to the appropriate service (data or phone). Unless they are patched to something, then they are not live. How to actually patch to phone or data varies depending on how the phone and internet service are wired to the wiring closet.

If they really just left the other ends dangling and unterminated, the best thing to do would be to terminate the to a patch panel like the one pictured (which is surprisingly easy with the right punch down tool)

If the jacks/wires are not labeled, you can trace (and test) them with a cable tester like this:

http://www.kleintools.com/catalog/cable-testers-accessories/vdv-scout-pro-tester-kit

this is just one example of a cable tester - there are lots of cable testers out there of varying quality, but this is moderately priced and works well for home use. There are cheaper testers that just use an array of LED's to show you the cable status, and there are (much) more expensive testers that will do a full cable qualification to certify that it will run at the rated speed. I've used this model and it works well for home use, one nice feature it has for cable tracing multiple cables is that it has several numbered terminators that you can plug into one end, then when you plug the meter into the other end, it will tell you which one it sees

My guess is these two Ethernets don't connect to each other; they both go to some third location yet undiscovered. Back in the old days, there was no WiFi, and there was an Ethernet run to everywhere you wanted networking, the runs went to a single location where you had a switch, router, DSL modem, possibly a server etc. This equipment took at least a shelf or two and had a cluttered, cables-everywhere hacker aesthetic. Probably near a phone line outlet since DSL was still king. A homebrew version of the "wiring closet" you have in offices today.

I would look at locations in your house where that would make sense or be likely to be "wife approved". It won't be a place you would ever want to put a TV.