If the specification given by Sandhound for your TV is correct then your television has an HD-15 connection as described here. You will have a similar port on your PC where your current monitor is connected. Is it these two ports that are connected together?
If the manual with the TV says 640 x 480 @60hz is the correct input then I'm afraid the picture you are getting with very large icons is as good as it gets. Getting a better graphics card won't help because the TV couldn't deal with a greater input anyway. To check that your current card can actually produce that output, try it on your current monitor and see what it looks like.
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Do you know that we're all in line for succession to the throne? Really?
Well, if forty-eight million, two hundred thousand, seven hundred and one people died I'd be Queen.