Not giving up is good!

To learn how to work with external eeproms try the I2C sample here
http://www.melabs.com/resources/samples.htm

Or wait till someone comes along that knows picaxe...

and this may help with the 595s.
http://www.picbasic.co.uk/forum/showthread.php?t=10200

Put something together in PBP and we will help you debug it.