The Nikon D3 Professional SLR Digital Camera features the exclusive FX-format CMOS sensor measuring 23.9 x 36mm which is nearly identical to the size of a 35mm film frame - thereby eliminating any significant crop factor or focal length multiplier...
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If you're looking at solely the camera body, and you either already have lenses or are planning on renting them, the Nikon D3 or D3s. You can find a used or refurbished Nikon D3 or possibly even a used D3s for just under $3000. They are full frame sensors that aren't jam packed with pixels; less pixel density = larger pixels = better light gathering. Here's a review of the D3:
They both excel in low light situations, with the D3s being the newer model with a slightly expanded ISO range and improved noise reduction.
But you're also going to need lenses, and fast lenses are expensive. If you go with the Nikon, you'll have blown your budget on the camera alone. Going with Charles' suggestion of the Canon 5D Mark II may be a good compromise; find a used or refurbished one to save money on the body. Then you might be able to pick up a Canon EF 70-200mm f/4L lens for long shots, and a Tamron 28-75mm f/2.8 for closer range shots, and still stay under $3000.
If you don't mind switching lenses more often, fast primes would be a good option too, in 50mm, 85mm, 100mm; all of them are reasonably priced.
Back to my first line: if you're going to spend this much, you may want to find a camera store in your area that rents pro equipment, and try one of these combinations out to see if it suits your needs before dumping a ton of money into purchasing. You may be able to rent a 5D Mark II and a good lens for <$200. Actually, there are mail order rental places now... TheLensPal is one (I haven't used them, so that's not an endorsement). You can rent a 5D Mark II for 4 days for $118. And lenses like the70-200mm f/4L IS USM are only $38 for 4 days, and the 24-70mm f/2.8L USM is $44 for 4 days. So yep, $200 for 2 lenses and the body for 4 days. I think that's probably worth it to try them out.
Does great in low light. Main differences between 7D and 5D:
vewfinder and revised body - other headline changes include a new AF system with a dedicated processor, dual Digic 4 processors and a new shutter mechanism to allow 8fps continuous shooting, and the ability to control groups of external flashguns using its built-in flash.
Canon EOS5D EOS 5 D EOS 5 D Mark II Digital SLR Camera Body with EF 70200mm 70200 mm 70 200 mm f/ 2 . 8 L IS II USM Canon EOS-5D Mark II Digital SLR Camera Body with EF 70-200mm f/2.8L IS II USM
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This camera really does an amazing job at shooting in any lighting condition but especially low light. It is a lightweight and compact full frame semi-pro camera with low noise at high ISO settings. It's a very affordable and competitive camera. The body offers protection against environmental hazards and weather. The HD video mode can shoot single and continuous images while recording. You'll like its usability even without the excellent low light capability.
21.1-megapixel full-frame CMOS sensor, 14-bit A/D conversion, wide range ISO setting 100-6400
Body only; lenses sold separately
DIGIC 4 Image Processor; high-performance 3.9 fps continuous shooting; Live View Function for stills
Full HD video capture at 1920x1080 resolution for up to 4GB per clip ; HDMI output
Updated EOS Integrated Cleaning System specifically designed to work with a full-frame sensor
The integration of HD movie capability into a high-end 21.1-megapixel camera opens a multitude of new possibilities for photojournalists and news photographers. With its full-frame CMOS sensor and outstanding ISO performance, the EOS 5D Mark II wi...
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Here is a camera that excels at low light shooting. This option is the body only, which is cool because it leaves a bit of room in your budget for the right lens (something with f/1.4 or larger aperture, like 24mm f/1.4, 35mm f/1.4, 50mm f/1.2, etc.)
The Mark II shoots extremely well at ISO 6400. ISO is expandable to 25,600, and people swear you can go out at night on a very dark night and get great pictures, even without a tripod. I can't vouch for that specifically, but I do know that this is an excellent camera that excels at low light shooting.
It should be perfect for your needs.