I have an LCD HDTV that has no DVI or HDMI input port; only component input
ports (Y, Pb, Pr), an S-video input port, and analog input ports.
I have a DVD player that upconverts the DVD picture to 1080i, but will
only send the up-processed signal out its HDMI port (not out the
component ports from which it will only send 480p).
Is there a way to convert the HDMI output from the DVD player to
a component input to attach to my TV so my TV can get the upcoverted picture?

Here is a discussion on your topic, of course they may be making all
this s**t up, but it sounds good to me! 
http://www.digitalhomecanada.com/forum/showthread.php?t=5540

Yes, it is possible to convert component video to DVI and HDMI. There
are special converters on the market, please refer to the links below:
http://www.lenexpo-electronics.com/detail.php?m_id=295&price=269.00

and you would also need a component video to VGA converter cable, just
like this one:
http://www.lenexpo-electronics.com/detail.php?m_id=446&price=27.99

Thank you