Intel core 2 was released in 2006, however most computers just started running it 3-4 years ago. Windows 7 was released in 2009. Although you can upgrade old computers to windows 7.
As far as cheap computers go, depends on if you are talking about a laptop or a computer and how much you plan to spend. Otherwise you could just get a i2-i3 or so processor, and upgrade to windows 7. Depends on what you want to do, personally I would rather buy a new computer than upgrade.
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Former multi-server mapper.