The only possible reason I can think of for it only happening when you play the radio is that as any electrical sensor begins to wear out, it requires just a bit more juice to operate properly.
When you turn on the radio, the small additional drain on the system takes away a little power from whatever sensor is going out, which would then send bad information to the computer, possibly causing all kinds of maladies to occur.
You also don't say if your system has a big amplifier attached, or anything like that that could cause an additional electrical drain.
In any event, you should be able to get some codes that will pinpoint the problem. Just do a search here on codes, or click on the link provided by ohfosho above, and you will get lots of information on how to pull them, and what they mean.