Ive a PS2 slim and a USB ADSL Voyager modem and wondering if anyone could help. How to i either connect the modem directly to the PS2 (USB to ethernet) or connect the PS2 to the modem via a router (USB with ethernet ports)
You can't connect a USB device to a system that does not support USB devices. The USB to Ethernet devices are to allow you to have an Ethernet cable connected to a USB port, not the other way around as the PC must have drivers running to control the USB port/device.
Your best bet is to discard the USB modem, buy a 4 port ADSL modem/router, a network card for your PC if it does not have one and connect both PS2 and PC to the router. This also means you don't have to have your PC on to play PS2 online.
There are several routers in the 40-50 pound mark that will do the trick. The Netgear DG834 is one such with a good reputation.
It is actually possible to use what you have (assuming your PC has a network port) by setting up ICS (internet connection sharing on the PC) and connecting yur PS2 to the PC via EThernet, but this is very unreliable and does not always work, and does mean your PC must be on for the PS2 to work.
Go the router route, it will be much simpler and more reliable.