Strange. Check your router's manual. From what I know, router's
control panel does not have this kind of setting whereby only one
computer can access the net at any time, since it defeats the
purpose of having a router.
Look for a small button at the back of router which says Reset.
It'll reset all your router's settings to default. If it still
cannot work, the router has a problem. Contact its manufacturer. If
it has been acting like that since you bought it, even more likely
it has a defect.