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Old hardware != Old software
Even if you can still access the Internet with Windows 3.1, it's not a good idea. To me, the number one criteria in selecting an OS to browse online with is probably if it's still maintained with security updates, etc. I'm not saying that you must use newer hardware; I'm saying you must use either Windows 2000 or later, or use a completely different OS such as Damn Small Linux which claims to be able to run on a "486DX with 16MB of Ram". Even with old technology on the hardware side, it's still possible to run new software if you choose well.