After a night connected to the computer I was happy to see two bars on the battery state icon. To play it safe I connected the reader to the USB port again... and was back to Low Battery. But I was able to open one book, just to check if everything works fine.
So the reader isn't stuck, it's a charger/battery problem. I tried to buy a replacement battery from Amazon.Uk but it seems it wont sell it to Italy or Germany

(possibly selling the item only in UK). eBay sellers are not so finicky and I was able to buy the battery here
http://cgi.ebay.it/SONY-PRS-500-PRS-...63616b0f1#shId
May be it's a little more expensive than buying the battery from HK or China, but in this way I avoid customs in Italy.
The PSP charger is not a problem, I will try to buy one in Thailand, if not there are easy to find in Italy.
Thanks to everyone for your help, I will post again when I get the charger, I suppose on the 5th of December.
Last update: suddenly the battery icon displays three bars and the reader seems to be OK

. Only I have no confidence that everything is fine, so battery will be changed and Ac charger bought.