PC would find you had no cookies on that computer so it would welcome you as a guest and invite you either to register (if you didn't have an account) or to log in (if you did).

I gather you logged in at some point but didn't check the "Remember me" box. In that case, your cookies would have been cleared from that particular computer as soon as you logged out (or went for an hour or so without any forum activity). What happened on the next computer would depend on what PC cookies, if any, you had there.