I also have this problem. I have discovered, however, that while I must plug the phone into a USB cable, that USB cable need not be plugged into a power source or anything at all. I can reliably (100% of the time) power up with a USB cable just laying in my drawer. I can also reliably (100% of the time) not power up without plugging into a USB cable.
In other news, I have also discovered that certain low-level actions tends to screw up lots of things. I can Odin just fine. I can flash ROMs, kernels, etc. just fine. However, I cannot restore a nandroid. Whenever I restore a nandroid, as best as I can tell, my partitioning gets all jacked up. When this happens, I can't do anything but boot into recovery (although once this happens, I can no longer flash ROMs) or Odin. Doing a full Odin flash restores functionality (in the sense that we all see where we need a USB cable to boot up), though. So ultimately, I think these phones have defective memory and that's what is ultimately causing this.
I bought this phone a couple days ago for $100 so I'm not out much (and can probably get most of that back even acknowledging the issues). Sure would have been nice for that person to have told me there were these issues. But oh well. C'est la vie!
---------- Post added at 10:06 AM ---------- Previous post was at 10:03 AM ----------
BTW, curious, what radio are you all using? I have only used EH03. I haven't yet tried EC09...