Do you have the right cable? We use a Radio Shack cable with an 1/8" headphone plug on one end and two RCA connectors on the other. You can make them, of course.
If the Kenwood has a phono section, how about trying it through the phono inputs.
I've had several mp3 players that have really low output voltage. They can sell them with any efficiency headphones they want to get volume, and there is no standard for output voltage.
If they're getting sound with no hum, I'd bet against it being a cabling issue.
Running it through a phono preamp is a great idea, that is if you want it to be terribly distorted by application of the RIAA equalization curve. The bass will be boosted enormously and the treble cut. The equalization is required because turntable styli cannot track full-amplitude bass. So, they're recorded with heavily attenuated bass regions, and then the EQ curve is applied in reverse as part of the phono preamp.
Another thought, in my truck, I run the MP3 player through the tape deck using one of those cassette converters with a wire and 1/8" headphone plug. Got ours at, can you guess? Radio Shack. Inexpensive and works great.
If you have a cassette player, you might buy the Radio Shack adaptor and try it, before going to the expense of buying a preamp.
This is another option which will work, but will not give the best sound quality. The S/N ratio for a cassette adaptor is between 50-70dB, whereas CD quality is 90-100dB. Big difference. They are cheap, I will grant you that, but you'll get cassette-quality sound. I do this in my truck as well, but with the engine and other noise, it sounds plenty good enough. In my livingroom I wouldn't do it.
There are two solutions which will not degrade the sound:
1) buy an mp3 player that will output line level voltage, enough to meet the input sensitivity of your preamp or
2) beg, borrow, steal or manufacture an op-amp gain stage to put between the mp3 player and preamp. You can make one with about $10 worth of parts. Like this one:
http://www.bobblick.com/techref/projects/preamp/preamp.html