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Where in the world are you. We are a United Kingdom based forum so not necessarily able to assist you directly, albeit that the principles of basic connectivity should be the same.
Most people leave their modems running 24/7 so that isn't likely to be your problem. It's going to be a network fault,, you're modem itself has worn out, or something on your PC - the last is probably the least likely if you have current antivivus and stuff.