The player is a Toshiba HD-A2. It has a 720p/1080i maximum output. If it had 1080p I wouldn't be getting rid of it!
Last time I used it, which was probably a year ago, it worked just fine. It's really slow to start up and really slow to read discs after you put them in the drive, but once it's up and running (probably 3-4 minutes from pressing eject to content playing) it works great.
I bought this thing back in 2007 during the height of the Blu Ray / HDDVD format war. I was a fan of the HDDVD side, so I put in my dollar vote. Sadly, my team lost, but it was fun while it lasted!
As to why I would have bought a 720p only player? I bought a 720p tv, so it didn't matter, and I was hoping HDDVD would win the format war, so I wouldn't have any issues buying a much better 1080p player later. Also, at the time, 1080p HDDVD players were silly expensive, so even more reason not to drop too much cash on something I can't take full advantage of yet.