With only $3K to spend and needing HDTV capability your only real choice is a used CRT projector. These are very large heavy devices and set-up is very critical. However, if your technical skills are on about the level of putting a new motherboard in a computer, you can do this yourself. A place called Encore! video advertises they have a bunch of low hour Sony VPH 1272Q's in stock. Most are priced ~$2500 or so. They are great for home theaters, so long as the room is completely dark. A ceiling mount will cost about $350 and figure on about $500 for a screen (lots of people like Draper screens with the 2.5 gain fabric). You'll also need a DVDO line doubler at about $600.
This puts you a bit over budget, but if you can completely darken your theater room, you'll be happy with the image this set-up provides.

MIKE