question about Monitor having DVI-D connector

Hopefully someone is tech-savvy enought to decipher this, but here goes!

My Syncmaster 171P LCD monitor has a DVI-D (digital only) connector as well as a standard VGA connector. I just recently used the DVI-D cable to connect to my video card's DVI port. Now as I understand it, DVI connectors are used to transmit HD video coming from say, a new HD DVD player? And correct me if I'm wrong, but LCD monitors can display 720p HD right? Now would either of these following scenarios work:

Hooking my LCD monitor up to a new HD DVD player using its DVI connector would display true HD (720p)?
and/or
Installing a new HD DVD-ROM (when they become available) into my computer and using the DVI cable from my monitor into my video card will display true HD (720p)?