This is an old post, preserved for reference.
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One of the problems with fixing old computers is dealing with the TV out. Most of the time, I used an LCD TV which has a variety of inputs, HDMI, VGA, SCART, components, composite, analogue and digital TV. This does a decent job with all but the analogue TV for older computers where it is sometimes a struggle to tune in, particularly having to use the remote to tune in. Most of the time, I use a composite video or RGB output which many of those computers provide. Here is a nice crisp clear colour video output from a rather poorly VIC20.