Windows ME was a gimmick brought out by microsoft to make use of the mellenium bug etc...
My advice is just get rid of the operating system, its full of bugs and security holes.
If that isn't possible then adding the dns settings should solve your problem. If you are using an eircom zyxel or netopia modem then they should have dhcp servers running and if so set your ip address to be assigned by dhcp and also your dns, then you should have no problems.