I have the same issues with my Loewe CRT except that it only accepts a HD signal through the VGA input and not through the componenet (this is by design and stated in the manual) I wanted to get a DVR and started looking at transcoders but they were expensive $400-$600 and most went the other way component source converted to DVI. DVI to HDMI required another box. There was one I found that I could use but it was too pricey $700+.
Google transcoder +DVI +HDMI
Cheers
Google transcoder +DVI +HDMI
Cheers