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Not having a PS2 (horrible thing
) I can't answer that much of your query.
Regarding connection to the ntl modem you will need to power off the modem each time you swap from lappy to PS2 or vice versa. Only one device can be used at a time.
If you are likely to switch regularly between PS2 and lappy, I'd recommend you get a router, to reduce the switchover hassle.