updating an old mac OS X 10.4 skype informed me that they no longer support OS X 10.4 Is it possible to update my computer or should I trash it. 
the processor is Dual 800 MHz powerPC G4 , 2MB SDRAM , Start up disc macintosh HD, Built around 2001.  It has 2 extra hard drives.

I would get a mac mini if I could use The 22" plasma screen monitor but it is connected with a large plug so I'm not sure it would work.
The latest supported OS on your computer looks to be 10.4.11
(looks like you have a Quicksilver (PowerMac3,5))

And if I'm not mistaken, Microsoft dropped Skype support for everything before Lion (10.7)

You may be able to get an adapter to plug your monitor in, depending on what that large plug is. Though that is really a separate question.