When you connect via HDMI it should only display the video modes which the tv outputs that are also accepted by the tv as inputs, when you connect by component the tv can't detect what inputs the tv uses and therefor offers all it has. It's possible that over some DVI ports HDMI is not able to detect the inputs the tv accepts.
If your video mode is set to an output that the tv doesn't accept over component, it may take a while but it should begin to cycle through them, if not try holding down the menu and the scroll up buttons down simultaneously on the remote for 10 seconds or so to force it to cycle through them.
It's really very strange that 3 tv's don't work over component, component while being the poorer brother quality wise is usually rock steady connection wise compared to HDMI, I feel there is something being overlooked here or you have 3 bad tv's or 3 bad sets of cables or 3 bad component ports on the tv's, any of which I'd find hard to accept.
They are definitely component connectors on the tv's are they, they are not composite, RGB, Y'Cb'Cr or professional connectors are they.