The Fuji F-10 is the only choice. It's the only small point&shoot with an ISO of 1600. Other than that, you would be looking at an SLR, which you already mentioned, or a digital SLR (dslr). PhilR...
The Fuji s602z is also capable of ISO 1600 and I can't think of a reason why I'd use the ISO 1600 noisy results over a stable, longer exposure taken with a tripod. I am speaking only to the quality of my camera at this ISO. But it would seem to me that a tripod is a pleasant alternative to buying an expensive DSLR. On my camera, the high ISO is achieved through binning (grouping the pixels) which means that the full resolution is no longer available. And you're still stuck with the noise. Mike..
The camera I would recommend is the Canon G6. For low light photos it would do well because it has an /2. F stop. This means that the lense opens wider than the standard lense, letting in more light. It has a 4X zoom from 35mm - 140mm.
The G6 is 7MP. Cost of around $600 or less. My boss has one and it is easy to use. (I am using the Fuji S3 and that is in a whole other ball park.) A review os here: http://www.dcviews.com/reviews/Canon-G6/Canon-G6-review.htm.
While I suppose it would depend on the college, but is there an "art" type department, etc. which may have access to better equipment or student photographers which may be able to help? If you are trying for stage type productions from a distance under actual performance conditions, a tripod will help but you are still dealing with a really difficult situation. Another alternative may be to coordinate the shots during a rehearsal or situation where better lighting can be arranged...
I use an Olympus C5050Z for this kind of photography.
ASA 400 (if needed) and f1.8 lens and a monopod..
If your budget allows I would suggest a Drebel for around $617 new from Buydig.com with a fast lens perhaps a prime like the 50mm F1.8 great for indoor lowlight with or without flash, for $69 or a zoom lens and a tripod. You would also have the option of other lenses later for other uses or different focal length...