For heavy keys with good Piano sounds, I think a stage piano would do. The only one I found at the correct prize-range was this:
http://www.zzounds.com/item--YAMP85
Unfortenatly, you will probably have a hard time playing Dream Theater/Symphony X on a stage Piano, I suspect, since it lacks most of the sounds that they're using, and doesn't even have a single lead sound.
The cheapest solution I found to be able to play all that stuff, and have weighted keys and good piano sounds, is with a MIDI controller and a good sound module. These are the ones I found:
http://www.thomann.de/gb/fatar_sl990_pro.htm (or
http://www.zzounds.com/item--MDOKEYSTAT88)
http://www.zzounds.com/item--YAMMOTIFRACKES
But, as you can see, that's quite abit above your budget...
I actually have a hard time thinking that you can find something with weighted keys, a good piano sound, and good sounds for the prog music for under $700. Perhaps if you buy anything second-hand, I never searched Ebay.
Hope that helped a little bit atleast
EDIT: I just noticed that none of those has built-in speakers, which means that you would either have to buy speakers too, or try to live with only being able to use a headset
EDIT 2:
http://www.thomann.de/gb/yamaha_dgx_530.htm (don't really know what "graded soft touch keys" mean. But 88 keys and "graded" usually means weighted... Atleast it's worth looking into