If by "night shots" you mean some sort of zero-visible light capture, I think your limited to Sony - some of their camcorders have a built-in infrared emitter providing "NightShot" or "SuperNightShot", monochrome video capture. The built-in IR emitter's throw is effectively around 8 feet but you can add an external IR illuminator (from Sony) to extend that a bit.
The HDR-HC9 is miniDV tape based and meets the technical requirements - assuming your computer has a firewire port (or you are able/willing to add one if the computer has no firewire port) - but it is more than your stated budget.
The HDR-CX500 series also meets your technical requirements - with the exception of $. Be aware that they save AVCHD compressed MTS files so your computer needs to be fairly beefy and the video editor should be pretty current and specify AVCHD file compatibility with the computing hardware environment.
If "night shot" is a different definition (as in "low visible light" level), the the Canon HF S series is worth a look.
The issue with high compression (AVCHD) is that it and fast action don't get along very well. For fast action you really want less compression (DV or HDV) applied to the video stream and at your specified budget, that is miniDV tape.
Consumer camcorders using flash memory and HDD for high definition video storage all use AVCHD compression to MTS files (or in JVC's case, TOD files).
Have you looked at any DSLRs that can capture video? I don't have much experience with them, but their video looks pretty good (assuming audio is not that big of a deal for you).
How about a "helmet cam"? The "VholdR ContourHD 1080p Full HD Helmet Camera" made it to my short list - though I expect its low-light behavior will not be very good at all...