Depends what what the modem / router shows as "good connection". Usually it is just layers one and two (physical and link/MAC), which may be just fine and dandy, but if layer three (IP layer) is not working then... nada.
Maybe the DHCP address is not being allocated, or is wrong, or the upstream router is faulty (at a layer three level), or DNS servers are down (or incorrect), or gateway is misconfigured, etc.
SD