Any way to recover data from a semi-bricked iPhone? My iPhone turns on, shows the white apple logo, and then after a few minutes shuts off. It is not a battery issue, it happens even when it's plugged in.

Is there any way I can get the data off the phone without resorting to a hard-drive recovery company?

Maybe some kind of program that can access the hard drive through the USB port? Or maybe I can open up the phone and somehow get the data off the hard drive?

I know that I can restore the phone through iTunes and have it working again. The problem is that I didn't back up the data so I have 400 or so notes saved only on the phone. If I restore it, they will be gone forever.

Just in case you are wondering, I haven't jailbroken or even attempted to jailbreak the phone. This problem just happened randomly while I was using the phone. It was frozen one day, I tried a hard reset, and ever since then I can never get it to work. I read that some people got the same issue via a remote wipe, however, I'm not subscribed to mobile me, so there is no way that could have happened.
If there is an Apple store in proximity, book an appointment with their tech. If PhoneView does not recognize the phone, I believe this may be your best chance to get the data out.