Why is only one of seven wires in my light box live?
This house needs AFCI breakers.  Badly.

It has old cloth-wrapped AC or MC cable, which has perished badly. You already see horrendous arc damage on one of the bottom wires; that kind of thing burns houses down.  And AFCI breakers detect that type of arc-faulting, and trip the breaker to stop it.  

That cable has to go.

Every single one of these cables has to be replaced.  Every one. All of it.  And then, you have to search the house for any other cables in comparable condition (or get the AFCI breakers and let them protect you). 

Stay with the good quality of work: metal jacketed cable/conduit and metal boxes. Clearly this site has environmental challenges where unarmored cable doesn't stand a chance.  If the cloth/rubber insulated wire is in good condition, that's fine, but it sure doesn't work here!!!  

I might attribute the damage to the cloth-jacketed left cable to rats -  but how would rats get inside a steel junction box with a cover?  In any case, I would not chance any unarmored cable in this house; I'd plan on continuing to use MC cable, AC cable, or metal conduit of one kind or another. 

Red-Taped Grounds

The purpose of the red tape is to defeat grounding (make the armored cable so it cannot carry ground).  That's done for one of two reasons. 


The good reason: If the supply cable back to the service panel is not grounded, you want to avoid connecting gronunds onward because that will create an island of grounds.  That means a ground-fault anywhere in the island won't trip the breaker (no way back to the panel) but will instead electrify all the grounds.  
The bad reason: The grounds do go all the way back to the main panel. But there is a hot-ground fault somewhere (in this wiring? How can that be? ;-b) and fault current is going back to the panel and tripping the breaker.  The repairman ignored the ground fault and stopped the breaker tripping by disconnecting the ground (!!!) which causes the island problem! 


The fix to the ground issue is assure grounds go back to the main panel (retrofit if necessary), restore grounds, and then deal with any ground faults (I think I know why that might be happening... :-)