If you installed an aftermarket receiver, then you would have had to bypass the factory premium sound amplifier. (Best Buy would have pulled an amplifier bypass harness off the shelf and used it to connect the two cables that connect to the factory amp.) If you're interested in good sound from your new receiver, it may be worth your while to run new speaker wiring, as the cabling running from the receiver to the amp was designed for low-level signals--not the speaker level signals you're using them for.
If you're interested in upgrading the sound without spending too much money or changing the OEM appearance, here's what I recommend:
Replacing the amplifier--this is the weakest part of the system, rated at about 7W RMS per channel. Cut the standard amplifier bypass harness in half, using one half for the line side amplifier connections and the other for the speaker connections. This way, you haven't detroyed any of the factory wiring. (I bought a 75RMSx4ch amp from Crutchfield--ask for the harness and you can get it for free.)
Replacing the back speakers--a good set of 3-way 6x8 Pioneer speakers can be had for less than $100.
Replacing the front speakers--I haven't found exactly what I want here yet, but these aren't a very high priority.
Use the information on shotimes.com to connect to the back of the factory radio--a set of female DSUB contacts from Radio Shack will make the connections to the pins on the receiver, and I bought a 3.5mm headphone jack and wired it so that I can plug in a CD/MP3 player, laptop, or whatever. If you do it right, plugging a cable into the jack will switch the sound source.
Hopefully there's something useful somewhere in this long post.
Dave