This is likely not the problem, but I thought I'd mention it for the newer people on the forum. The lcd side goes to sleep mode quite quickly and takes a couple seconds to come back to life (you can also press the menu button to do this manually)... are you sure that wasn't the case? And, if you are trying to reboot when it is still on and/or shut down too quickly, it can affect the power cycling.

I had something similar happen one day when I was somewhat distracted and impatient. I actually thought it had shut down when it hadn't. Instead of waking it up (menu button press) I pressed the power button to reboot, and nothing seemed to happen (I didn't wait long enough for it to wake up), so pressed the power button again, and then a couple more times, but nothing was happening. When I realized what I might have done, I let it sit for a bit to make sure it wasn't working on something. When I was sure it was off, I reset the battery, which did fix the problem for me.

To avoid me having the problem, again, I always wake the lcd side up before I shut down and I haven't had the problem since.