That takes the input signal and splits it into all the outputs.

Are there two ethernet ports at every drop or one? If not, the good news is that you can probably reterminate the jacks into RJ45 (telephone is RJ11). You'll need something like this: http://www.westsidewholesale.com/leviton-47603-c5.html

You should be able to buy the block made specifically for the box where the cables are terminated. Look for a manufacturer.

You'll also probably need to reterminate in the rooms too. You'll use RJ45 jacks - keystones if the jacks are modular or new plates. You'll need a punch down tool (http://www.homedepot.com/p/Ideal-Punchdown-Tool-with-110-and-66-Blades-35-485/203761571/).

Terminate both sides in TIA/EIA-568B. The jacks and panel will be labeled by color. Keep the pairs twisted as much as possible when punching down.