Capped off outlets and light switch wiring, now no power to half the house
I would feel somewhat more comfortable if you had found three hot cables, and each cablewas turned off by a different breaker.  As things are now, you have not, and you must be careful that you do not accidentally connect two breakers nose to nose, feeding power in one breaker and out another.  That will either create a loud flash-bang, or seem to work but then create a lurking safety hazard that can start a fire.  

I would expect that one of your four "dead" ones is in fact live, and something has gone wrong with your testing method. 

I am fond of dollar store nightlights and cheapie extension cords.  I cut off the plug (part with the blades) and throw it in the trash.   Then, I take the rest of the cord and split the wires and strip each wire 3/4".   Then I wire-nut it onto a hot and neutral I aim to test, and plug in a nightlight or a radio, then see if I can energize the circuit. 

Anyway, 3 breakers, 6 cables, makes sense.  3 of them would be supply side from the breaker (possibly stopping at intermediate points first) and 3 would be onward power from each of those circuits.   I would identify every one of your 3 supply lines, as best you can, using the extension cord trick rather than a non-contact tester. 

Also for each of the 3 circuits, figure out what sockets or fixed loads each bris powering now.  The ultimate goal is to identify all  the loads connected to each of the six sections of cable.   

Now, turn off all of the three breakers but one. Run a cable from the hot wire over to one of the 3?4? mystery sub-circuits.  Then search the house and find out which sockets or loads that circuit powers up.  Mark accordingly.  

Once you have mapped them, there will probably be some logic to how they are wired and how to match them up.