Terrible Problems with internet ongoing for years

I have had problems with internet for years in this new house i moved into, and it is horrible because I need it for homework as well as just playing games. I have recently bought a new router to try to solve the problem, but my step dad also bought an all-in-one modem. Sometimes the new router network works, and sometimes it doesn't work but strangely allows me to use things such as skype, but not servers like google or games. It also says connected under internet, but disconnected on the network genie. It says DNS isnt working, sometimes DHCP too. All I wan't is internet, how can you guys help me???

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