Serial.list() with a capital S.  list() is a class method not an instance method - Google those if that doesn't make sense I can't explain it well in a few sentences.

Doh!   Typical noob mistake, I suppose.  That made the error message go away.  Still didn't give me a list of my COM ports though...

Do you have the arduino plugged in and powered? It's possible that your system (if it's newish) doesn't have any physical serial ports.

Sorry, this might be a really stupid thing to ask but you're clear that what I posted wasn't a numbered list of different things to try?  Paste lines 1-6 into a fresh sketch and run it.

I get the same warning about versions of RXTX but I also get a list of serial ports.

LOL!  Yes, I was aware that it was a whole sketch, not a list of seperate items.  I typed it in, commented out each line, then ran it over and over to see how the error messages would change with the addition of each new line, running first line 1, then 1 + 2, then 1 + 2 + 3, and so on with the results as above.  No list of ports. :-(  Maybe it's more to do with the machine than processing.  I did have a similar setup running on a crappy old XP pentium which gave up the ghost some months ago, and things seemed to work fine then, at least intermittently.  This is a brand new beastie, Fujitsu DTL1-02990 running Windows 7, so the OpSys is new as well as the machine.  It's got to be a compatibility problem of some sort, especially if the code works for you.  Thanks for you assistance, anyway.  You are very kind.

Sorry, it's a fine line between assuming missing knowledge and asking insulting questions ;).  Are you running the Arduino IDE at the same time?  That might be blocking access to the serial port although it's weird that you can't see any serial ports.

I've tried it with and without the Arduino IDE running, with the same results.  I'll try wiping and re-installing processing, and see what happens.  Cheers!