The problem you're having is that you're comparing apples to oranges.
To put it simply: DVI/HDMI is a digital signal and component is an analog signal.
To do what you want, you need more than a switch. You need something a bit more complex to convert the digital HDMI to an analog component video signal.
THIS claims to be able to do that but I've never used it myself. The upside is that it also takes care of your (two channel) audio as well.
Likewise, converting HDMI to DVI is a bit simpler as both are digital formats.
THIS claims to do that but, again, I've never used it. The drawback to this is that it won't pass any sound from the HDMI signal (DVI doesn't pass audio to begin with). You'll need to take that directly from your source.
Using these, you can utilize both your DVI and component inputs on the TV without the need of an external switch.