Based on what I've seen around the internet, in print, and especially in Apple's and eBay's writing, it seems they should be capitalized as they appear, even when at the beginning of a sentence:

 eBay is a great auction site. is correct.
 EBay is a great auction site. is incorrect.
 Ebay is a great auction site. is also incorrect.
 EBAY is a great auction site. is super duper incorrect.

eBay example: About eBay, "eBay is The World's Online Marketplace®, enabling trade on a local, national and international basis."
Apple example: , "iMac comes with iLife ’06, a suite of easy-to-use applications that make the spectacular part of your everyday life."
Both accessed 6 June 2006.

As for typing in ALLCAPS ... well, that is bad style, anyway. I don't think any way would be "more correct" in an already incorrect situation like that, so I'll say nothing.

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