What can I do with the storage spaces under my radio?

[Izman1000]

Please Help-

So, I finally got around to hard-wiring the GPS in today and ran into a snag. I'm sure it's got something to do with the different types of electrical currents in the car, but quite frankly, I'm very amateurish at this kind of thing.

Here's my issue...
As you can see in the pics, the GPS was running into the cigarette light. Today I pulled the stereo out, cut the end off of the cigarette adapter and tried to connect the GPS with the acc and/or battery connection running to the stereo... No power.

What is wrong...
Is the type of electrical current running to the cigarette lighter different than to the stereo?
What can I do?

Thanks in advance.