At the moment your internet is slow/can't access google, can you go over to your windows PC and check. Perhaps it is the ISP's problem.
With the Airport, it might not reach everywhere especially if you have a big house, e.g 3000sq ft. The best is try to put the Airport in a centralize location.(main floor)
Getting a new router does not necessary mean your problems will go away. All router/Wireless are industry standard and suppose to work with all equipments.