Hello Richard,
To enable network support in Windows Vista, you should install a driver for the network card inside Vista. To do this, you should go through the following steps:
1. Connect Parallels Tools CD image (vmtools.iso) to VM. You can find
Parallels Tools CD image at the /Library/Parallels/Tools folder.
2. In the Windows Vista Start menu, go to Control Panel -> System -> Device Manager and select Network Adapters -> Parallels Network Adapter in the left panel. Double click it.
3. Choose Driver -> Update Driver... -> Browse for driver software on your computer. Point the path to your CD.
4. When Windows asks you what driver to use, you should point to:
Drivers/Network/RTL8029/Win2000.XP.ME.2003 on your virtual CD-ROM.
Best regards,
Xenos