There are a couple of potential spots to look at. First, get rid of the small gauge power wire. Starving a stereo for power WILL cause a shut down on many models. BeGreen also has a good point. To test the impedance issue is pretty easy. Follow me if you will:
1st - do you have left/right AND front/rear control of the speakers? If yes, then impedance is probably not your problem because most stereos that have 4 channels will also handle 4 ohm speakers, and that is typically the lowest impedance speakers on the store shelves. This is assuming that you have 4 matched (impedance) speakers of either 4 or 8 ohm.
2nd - if you only have left/right control then you could have a problem with a 4 speaker arrangement. This could happen if you had 4 4ohm speakers connected in parallel, giving a total impedance load of 2ohms per channel. Most run of the mill stereos/amps will NOT hold a stable 2 ohm load. This will cause excessive draw on the stereos amp and create a high temp or shut down (or burn up) scenario especially at higher volumes. (the more the speaker cone moves in and out, the greater “swing” of your impedance).
Hope this makes sense. Step 1 and 2 does not cover all possible impedance issues, but for run of the mill components it will hold pretty true. It is also possible, but not as likely that one of your speakers has had a voice coil short out somewhere in the winding. This can cause very strange things to happen, too long to type.
And - it is possible that you are expecting too much from your stereo, and adding more power (oooh, oooh) is the only choice.
p.s. I am a stereo super freak. My 73 challenger has a 17 speaker (odd number because of front surround stage), 3 amplifiers, electronic sound processor (for surround sound) and fully adjustable freq. control board. Oh, and it gets its power feed from a 2 gauge welding cable. Lets not go into the home stereo.