And I mean CHEAP.

Anyone have a recommended camera that costs less than $100 and uses a rechargeable battery? Bonus points if it focuses quickly (ie, no 5 second pause to hold the button before you can take the photo), works during a blizzard in temperatures under 15 F, and can take 3-4 hours of photos/600+ photos on a single charge.

I have a Kodak EasyShare for work, it runs on AAs (which it is eating through), half of the photos are blurry, and something mechanical can't move when it gets cold out. Since I've occasionally had to inspect multiple properties in blizzards in Utah/Wyoming/etc, it really isn't ideal. I'm trying to replace it but haven't found great stuff at this price limit. Which doesn't surprise me at all, but if anyone missed my post the other day my company is on the warpath when it comes to finances.