I had almost exactly the same experience as you a couple of months ago. I'd dug out the PRS-505 (having been using the 350 exclusively for a while), found I couldn't get the battery to hold a charge, order a replacement and fitted it, only to find that it
still wouldn't hold a charge. Unfortunately I also managed to snap the plastic plate housing the connectors at the bottom of the device
I then put it away again and continued with just the 350.
However, just a few days ago I unearthed it once more, with the intention of perhaps eBaying it as "for spares or repair". This time it charged up with no problem whatsoever, and I've been enjoying using it immensely ever since (the battery indicator is still showing full).
The only thing I can think of to explain this is how I charged it up. Although I can't be certain, I strongly suspect that when I was having the issues previously, I had used a USB cable connected into a wall adapter, as I often charge USB devices in this way. This time, however, I charged it with the USB cable plugged directly into the computer.
When it finally runs down again, I'll try charging it from the USB wall adapter again to test the theory.
Garry