Why can't my 32" Sony LCD show component out?

Your DVD output may not going to component out (assuming your cables are ok-check the other DVD outputs on the TV). It may be going to s-video out or composite out (I gave a buddy a Toshiba DVD player and had the same problem). Check the manual or the menu. You'll be fine.

I have been thinking about a pair of these for my desktop to use for both HDTV and as computer monitors.

Avguygeorge and others - you didn't like them?

"In this set up you can only play originally recorded HDDVDs but older formats you'll need to upsample. You'll need to buy an upsampling DVD player which is about $50 worth
Marakanetz"

I hope this was a joke otherwise your ideas and experience is scary. If what you said was true and ITS NOT then analog cable and TV or VHS would not be viewable. If there is some feature I a missing I will say sorry but I have never ever heard of that and I have several both Sony and non Sony HD units that can play any signal.
Also look for "Progressive or 480P" output on DVD or in menu because it may be set to 480I which as others said is for S video and composite. Could also be the DVD player isnt working right or your inputs may need asigned on monitor or even a problem with Tv itself.

In case some don't know; this IS an up converting tv. ---AS most all tvs are,now a days.--To see up converting in action one needs only to pause a vhs tape. On the older sets,pausing a tape reveals you are seeing 1/2 the frames and naturally the quality goes down.
I had a large crt/rpt and wanted to see what a top lcd looked like.--this set is one-- However I never intended to keep this set and have since purchased the Pio/kuro 6020.
Which in my mine is way above anything lcd.