network printing from my new windows pc using a HP 710 attached to a networked Vista pc

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My setup worked perfectly when I had an xp pc and a vista vc.

The xp pc had a samsung 6060 laser printer connected by a parallel cable and the vista pc had a HP710C also connected by a parallel cable. I also have a laptop running ubuntu linux. The pcs are networked peer to peer and connected to the internet through a wired router. I was able to share files between all three machines, and print on any printer from any pc.

I now have a new pc running windows 7 (64)and one of the many problems I am having is getting the printing to work.

The two pcs can share files ok, I can find and install both printers on both pcs and they both print through the pcs they are attached to. What they won't do is print through the network. though I can select the printers in an application and press print nothing then happens (not even an error message) I am not a pc 'teckie' and don't really understand how it should work, but have tried a variety of things like 'permissions', 'firewalls' and all the automated fault finding fixes,  and so on but have struggled trying to understand what kind of driver should go where, or even to identify if this is a network issue or a printer driver issue

I'm tearing my hair out! And I've given up on networking the linux machine, and parked all the issues I am having with user account control, permissions and file ownership. 

Can anyone help on the printing front please? Thanks.