I just bought a Sony PRS-700 and I've been having similar, though not as extreme, issues. It looks to me like it's a battery or electronic problem. When I first charged it, I had to have it charging for 5 hours and then overnight. After the 5 hour charge, from a wall charger, the screen was frozen. But, the red light was on supposedly indicating that it was charging. I then plugged it into my laptop USB overnight and it seemed to work OK.
However, I noticed after a couple days that the battery meter was showing that it already needed to be charged. I had only turned 20 or 30 pages, way way below their quote of 7000 page turns. So, I plugged it in and charged it up again. But, again, after 2-3 days the battery meter indicated it could be charged again. This time I had only read a few pages. It seemed to me that the battery has a high discharge rate (maybe due to a leakage current?).
Now at home, I plugged it into my home desktop USB port overnight. This time, when I turned it on in the morning, the battery meter was lower than the night before.
I'm concerned that the battery is bad. I plan to call Sony about this later today.
ddave