While others have posted on the impossibility of setting up a quality astrophotography rig for $1000, it might be worth focusing instead on what this guy CAN do with $1000.
I would like to hear suggestions from others, but here are some example of what I'm thinking about: Time-lapse photos of meteor showers. Timing of occultation events (e.g. when the moon just grazes a star, giving information about the contours of the lunar surface). Searching for new comets. Observation (indirect, of course!) of sunspots and solar flares. Quirky efforts like year-long time lapse photos to illustrate the analemma, e.g.:
http://antwrp.gsfc.nasa.gov/apod/ap020709.htmlMan-made objects can be a lot of fun, too. Photos of the silhouette of the ISS, if one is lucky enough to be in the correct position as it passes in front of the sun or moon. Heck, just watching satellites fly overhead, especially Iridium satellites as they flare, and the ISS when the shuttle's docked (with the combination being about as bright as Venus these days), and the heavens-above.com website is a big help with all that.
I recommend browsing through previous Astronomy Pictures of the Day (
http://antwrp.gsfc.nasa.gov/apod/ ) to get some ideas. A lot of it is professional astrophotography but some of it is the work of dedicated amateurs, some of whom didn't have >$1000 rigs.