this occured within a few days of us beginning to use the wifi facility in a nintendo wii. Is this a coincidence?
well since you have just had it working for a little while, the next step would seem to be to NOT turn on the Wii or the working laptop at all!
Try connecting the HP laptop to the router using WiFi and leave it to soak-test. Does it still work after 30 mins? 60 mins? A full day?
Once you have established that there is not an inherent time-based problem with the HP laptop talking to the router then you can start adding the other devices.
EDIT:
One thing that occurs to me. We had a problem here where one of our computers was dropping off the WiFi; wasn't an issue with the other three WiFi machines, only this particular one.
Finally tracked it down to the fact that one of our neighbours had just purchased a WiFi router and was running it on the same channel as ours and the suspect machine was the only one that was in such a position that it was getting confused as to which network it was supposed to be connected.