Actually it probably has less to do with the cable and the player, and more to do with the fact that they are MP3's you're listening to. MP3's by their very nature are compressed and lose sound quality in the process. Some MP3's are more compressed than others and perhaps the MP3's you have are very compressed. This would explain the sound you're explaining (?).
How did you get those MP3's? Did you rip them from a CD? At what frequency were they recorded? The higher the frequency, the better...but then again the better the sound quality the less compression that is used; and therefore the more space these take up. You'll have to find a the most adequate compression frequency vs. file size vs. sound quality.
I think it's the actual files because very rarely will a cable has as big effect as you are describing, and also that effect you're describing (sound being washed out) is often characteristic of MP3's. The files often lose a lot on the ends, bass and treble, and perhaps you never noticed these compression effects because you had never listened to the MP3's on a speaker system before (?). Headphones have a hard time conveying the same sound range as a speaker system, so it may never have occurred to you what these files would sound like on a speaker system.
I recommend, if you have another speaker system somewhere that has an aux input (most do these days), perhaps in your house/apartment, you can test out your MP3 player on this as well. If it still sounds washed out, you know it's not the patriot and you can narrower it down to the cable, the MP3 player, or the actual MP3 files (would be my vote). Then you can get another cable, if you so desire, to compare.
If in the end after doing that it still sounds bad, the only recommendation I would make to you is to re-rip the files from whatever CD you got them originally. But do it it at a higher frequency as this will only improve sound quality (assuming that's how you got the files in the first place). Perhaps as a test, you could only rip one song for comparison at a higher frequency and then compare it to the old file you have on your player. I hope you figure out the cause of the issue.