Total of 12 strands, 4 each of the above wires. And Im installing a ceiling fan, that has a black wire, white wire, blue wire, and green ground. But I forgot to look at the hookup, when I pulled the caps off the ends, to pull them around the brace. Now various lights on the circuit won't work, and I can't seem to get the fan operating, even though I mnaged to get the light to come on. Can anyone tell me how I need to hook these all up to complete the circuit?

Must be a very large ceiling box to have that many wires. You are going to have to do a little detective work to sort this out. How are the existing lights controlled? Is there a wall switch? If so, you need to use a Volt Ohm Meter(VOM) to find what one supplies power to the box. When you do that, hot incoming black to fan black and fan blue, white to white, ground to ground, all other black leads together. If the wall switch used to control all the lights, then you can pull a pigtail from the hot and wire as before. However, there is no way to have the fan run and the lights off. If you just have pull chains, you will need to find a constant hot, connect the fan black and blue to it, white to white and ground etc. That way, lights are on a switch and fan and fan light controlled by the fan pull chains. You may also have a switch loop in the circuit so that adds another variable. As I said, use a VOM to pinpoint the circuits in the ceiling box.

With 4 3-wire cables and no idea what they do you would be best served by having an electrician come in and sort things out.
Unless you are real good at tracing and troubleshooting electrical this will be a nightmare for you.
The +/-$200 will be well spent.

Ok, only 1 black is registering a current of the 4. The wall mounted light switch it leads to is a dimmer switch. And the lights that are on the same circuit are still non-functional. That gives me one strand that has a current.. any ideas? I tried hooking the blue first, then the black wire to the hot black, with the white from the fan on the white from the strand connected, and had no luck.

If the dimmer controlled the lights, you can't use it to control a fan motor. It sounds like you are trying to intercept a switched power feed to control the fan and light. If you have 1 hot, you will not be able to run lights and fan/light. Was a light on this box? controlled by the dimmer?

OK, so you have four cables, each with a black, white and ground wire, in a ceiling box. Now we need to know how many wires there are in the switch box and how they are connected.