No.
Your budget basically gets us to low end (maybe mid-range) of the consumer camcorder area - or maybe helmet cams,
The biggest hurdles in your requirements - based on the budget you set for us - will be:
8 hour charge (need to use optional high capacity batteries from the camcorder manufacture for long charge time - not the battery that came in the box with the camcorder).
Stable image when handheld and running. Stabilizer vest systems (Steadicam, Glidecam, and many others) would be required.
"Does well in low light"... means LARGE lenses and LARGE imaging chip (3CCD or 3CMOS) arrays - not the less than 37mm lens filter diameter lenses and 1/6" single CMOS chips in consumer cams in your price range.
There are no "ruggedized" consumer camcorders that will "guarantee" no breakage from dropping.
The closest I can get you is a helmet cam - the GoPro or the Contour HD might work - if properly mounted to you. Your body becomes the "stabilizer", but with running, this will make the viewer ill. And as far as I know, neither has any useful zoom and low light behavior is not good at all.
In either case, shipping is not a big deal - as long as the camcorder is packed properly.
A camcorder that:
-Can hold a charge for 8 hours (work day)
-Handles a lot of shaking (running while filming moving person) that will not leave you sick when reviewing
-Removeable memory that can hold multiple hours of recording (8 hours would be perfect)
-Can handle 50 weeks of travel a year through airports, sometimes being shipped parcel to job site
-Good zoom (following moving subjects sometimes 150 ft away)
-Hand held
-Does well in low light environments
-Durable (7" concrete floors just waiting for a drop)
-Final recording does not have to be professional grade, but viewable
-Under $500?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic