Of course, you took the battery out for a few minutes?
If you connect a charger while the phone is completely off do you see the charging graphic, and does the phone appear to be charging?
If you can't boot into Download mode you really don't have many options. You could buy a JIG as a last ditch effort to get the phone to boot into Download mode. Otherwise, a JTAG service (ex.
http://mobiletechvideos.mybigcommerce.com/samsung-galaxy-s-iii-jtag-brick-repair/) might be able to recover it.
Of course, it should still be within the one year manufacturer warranty - I'm sure Samsung would be happy to give you some excuse about why they can't repair it for free, and how you damaged it by dropping it or some equally lame excuse (uh, I mean, they'd be happy to honor their warranty and just bill you for shipping, and it'll be returned in 4-6 weeks - yeah, that's what I meant!).
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