Check your rear speakers to see if the magnet has fallen off of the tweeter portion of the speaker. That is common on the speakers in the 850's. I just fixed the rear deck speakers in my '95 850 sedan. These small magnets had fallen off the the back of the tweeter (or midrange) speaker insert down onto the main speaker cone. I reattached the magnets with a gel epoxy. Both rear deck speakers had this same condition and now they sound like they used to! Also, my radio has the "premium sound system" logo and I do not have an amplifier.

Are you sure you have an external amp? Slide the radio out, and look for a round black cable (other than the antenna cable!) plugged into a connector marked "amp" . If you don't have this, you don't have an external amp. Many of the double-din sized Volvo radios (whether or not marked "premium sound") did not need external amps, although the amp was an option.
If you have the amp cable, you can follow it to the amp, or you can get the factory wiring diagrams which will show you where the amp should be.
You may just have factory speakers decomposing after 8 years, or a wirng glitch from fraying (not all that unusual in door speakers, for example, where the wires are flexed with opening the door).
You can try getting a good speaker of the proper ohm rating, disconnecting the original speaker, and temporarily connecting the test speaker--if the sound improves, it's likely the speakers,not the amp or wiring.
Post what you find--it may help the next guy.
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We have met the enemy and they is us. [Pogo] S70 T5 cop car : Rough Rider suspension, Walmart fog lights, eBay speakers, ambiance by Pall Mall, trim by Le Duc d'Tape, 8-channel THD by OEM amps