I have a 1080i/720p lcd television. If I were to buy a 1080p unconvert dvd player, would it display at 1080i? I've seen lots of 1080p upconvert dvd players at a lower cost than the ones that say they'll do 1080i/720p.

1080p upconvert players will also give you the option of outputting 720p or 1080i. Your TV will likely not accept a 1080p input. LCDs are fixed pixel displays, so they convert all inputs to their native resolution (probably 720p or 768p). By a 1080i/720p display, that only means it accepts those resolutions; it doesn't mean it displays those resolutions. You're probably best off outputting 720p from a player.

I have a 1080i/720p lcd television. If I were to buy a 1080p unconvert dvd player, would it display at 1080i? I've seen lots of 1080p upconvert dvd players at a lower cost than the ones that say they'll do 1080i/720p.

Yes, 1080i is always an option.

-Bill