Okie,

If the speakers have been used with the stereo before, there are only a couple possible answers. Speaker wires are fouled (shorted), you have connected the speaker wires backwards (cross phased), the speakers are crapped out, or the head unit is fouled.
What you need to check:
If you have a multimeter, or have access to one, check the continuity between the speaker cables. (+) - (+), (-) - (-), (+) - (-), and all to ground. This will check your speaker wires.
Do a resistance check of your speakers. Should be 3.5 - 4.5 ohms (speaker resistance is never perfectly 4 ohms).
If your wires check out, and your speakers check out, make sure your wires at the back of the radio are in correctly and that you don't have the polarity crossed on one of them (+) or (-). If just one of your speakers is reverse phased, it throws the internal amp for a loop and you get horribly distorted sound.
Try fading the stereo forward to aft, at high volume, then left to right. If it starts clearing up when you do that, then a speaker is out of phase.
If everything is well, no issues in any of these parts, then it is time to get your radio checked or replaced.

DO NOT replace anything until you have checked everything.

Work smart, not hard, and keep what money you can.

Hope this helps.