There are convertors but from what I have seen they are expensive. (Over $170)
component out on the DVD player won't help, the TV needs to accept component in.
As far as it working on SD with component, I will find out tonight. I won't get access to my HD TV for a few more weeks (moving) so until then I need to use the TV at the corp apartment. In about another 2 hours I will be trying it. I will post an update regardless.