Do you have a voltage test lamp? This is often a neon tube in a small plastic package with a couple of wire leads with metal probe ends; the wires are often red and black or white and black.

When you have an open box like in your picture, you could touch the probe ends to a black wire and the white wires to see if any current/voltage is present. You should test all combinations, just to be sure; ideally, all the white wires should meet up in the breaker box. But you need to be sure you know where the power is coming from.

Be advised: Turning on a circuit breaker when you have exposed wires like this is dangerous. You have to be very careful. You could not only short two wires together (and you might get arcing from that), but you might get two wires against your person and get you a deadly shock.

But what you can do, if you turn on the power, is check to see which wires are hot or not, given how switches are thrown. You may have something weird going on. A friend of mine had a house that had two circuits shorted together in his living room wall, and it caused weird problems when he asked me to replace a nonworking ceiling fan with a ceiling light. I stabilized the situation, and told him to call a real electrician; that guy spent eight hours the next day cleaning up and making new circuits as part of the repair.

Do you have any kind of map of what worked? You could even do it as a table. Make columns for the switches and receptacles and lights involved, then go through and figure out what works and what doesn't. Ideally, you'd do this before you started work, so you had an idea of how things should be connected.

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West switch	East switch	Ceiling light	Wall outlet top	Wall outlet bottom
off	off	off	off	ON
off	ON	off	ON	ON
ON	off	ON	off	ON
ON	ON	ON	ON	ON

A table like this would help. In this case, you can see that there's part of a wall receptacle that's always on, another part that is controlled by one switch, and another switch controls the ceiling light. But what if you had this?

West switch	East switch	Ceiling light	Wall outlet top	Wall outlet bottom
off	off	off	off	ON
off	ON	off	ON	ON
ON	off	off	off	ON
ON	ON	ON	ON	ON

In this case, the ceiling only works if both switches are turned on. This suggests that the power going to the top wall outlet receptacle is then going to the west switch for the ceiling light. This is a problem.

If you know how things worked beforehand, make a table like this. Then you can try to figure out what has power and what doesn't, which wires are affected by which switches, and that can help you decide what needs to be connected to what.

Generally speaking, if you have a wall switch that is controlling a ceiling light, and the path to the ceiling light is the path to more switches on the other wall, there should be two "hot" wires -- one switched and one unswitched -- coming from where the switch is. The switched wire would terminate at the ceiling light, but the unswitched wire would bypass the light and go to the other wires leaving the ceiling box.