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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.
 
Try changing the wireless channel. Sometimes certain channels don't work well with Macs and can cause slowdowns or dropped connections.
 
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