When you say "new downloads", do you mean that you can't listen files that have been fully downloaded or files that are being downloaded?
Have you tried running the software update function from the System Preferences in order to get the latest version of Java?
If you did and still get that I would suggest you try again to launch a file that you are downloading and then wait for a couple of minutes. If you suddenly hear it playing after a while then it means that something is taking up too much RAM and the Player is too slow.

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iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

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