Monitor System requirements for Full HD support?

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http://superuser.com – I have a Compaq Laptop which is 4 years old. It have a maximum resolution of 1280x800. The laptop do not have any dedicated graphics card. I recently bought a Dell S2240L Full HD LED Monitor. When I give the monitor to full HD i.e 1920x1080 there is some flickering in the screen. I took it to a local computer shop to check for the problem. They said that its because that the system does not support the resolution. So I am planning to buy a new laptop. I would like to know what is the requirements for a system to support full HD. Also what models are available for the same. Any help will be a (HowTos)