Audio Systems: Unknown power problem, factory speakers, rms power

Question
I have a 2003 Kia Sportage.  I recently noticed that upon turning the volume up all speakers would become very distorted.  At first I thought the speakers were blown but upon further testing found that they weren't.  Eliminating the speakers I could only think of the CD player itself, which I replaced.  With the new player installed the speakers still become distorted at even medium volume, I'm stumped and I don't like it.  

Answer
Provided it does not have a factory amp, you probably are asking more of those factory speakers than they can deliver.

You may be hearing the distortion for two different reasons.
1) speakers are damaged.
2) The decks' amp is clipping before it even gets to the speakers (underpowered). Be sure that the deck can provide the RMS power requirements of the speakers.

Despite your tests:
Run new speaker wiring and if that does not cure it, install new speakers.