The HV-32P37 is most definitely 1080i HD capable (as are all the JVC HV series sets), but only through component inputs.
Note that the pictures of the set on the ebay listings are incorrect - the TV pictured in the listings is a HV-36P37, which looks very different...
Here's a review, but bear in mind the set was reviewed at £1100!
http://www.homecinemachoice.com/cgi-bin/displayreview.php?reviewid=3727
If you do a search, there is a lot of discussion about these sets on here, going back a few years. They are capable of some very high quality pictures, but poorer quality sources, i.e. poor freeview/Sky channels, can suffer as the picture is upscaled by the DIST processing. However, I have found that with careful experimentation with the many DIST settings, a good quality picture can be obtained from most sources.
Despite these reservations, there are times when this set really excells. I have a progressive scan DVD player connected to my set via component, and with this setup, the PQ of a good DVD is quite amazing.
I intend to connect the set to the HD component output of my PC when I get round to it...