I have an Explorer 3250HD Scientific Atlantic cable-box connected to a 42" Panasonic Plasma via an HDMI to DVI video cable. The picture quality is much worse than when it was connected with a regular component cable. Is it possible that my inexpensive 25$ cable is worse than the standard component cable?h

No, but it is very possible that the combination of that TV with that STB, component is the way to go. HDMI doesn't always have the best PQ.;)

Agreed, you can have quality wire with a crappy implementation.