If it's just a router - yes. If it's a router with built-in ADSL modem - no.
AFAIK, if you don't know the router password, a 'factory reset' should fix it. Not sure about that, so someone might correct me.
Edit:- As above ^^^^ - of course this requires a PC (either your old one or the lappy) connected by wire to set things up before you go 'wireless'