It is very common for home routers to hang up in the manner you describe, particularly in response to power glitches. Unplugging the router for 30 seconds then reconnecting it clears the problem most of the time. If you reset the router (and modem, if there is a separate DSL, Cable, or Wireless modem) and still have limited connectivity after two or three minutes you probably need to scan for infections - post a request for help in the "Am I Infected"
forum to get it checked out. Once your system has a clean bill of health post back here if your net still isn't working.