Well, I have replaced the battery today. The procedure was not very hard, the main thing is to remove the entire LCD as the battery is stuck to it with pretty strong tape. So you should remove the LCD and use a tool to separate the old battery from the LCD, I am sure that if you try to force it out without doing this you will crack the LCD. The soldering is very simple.
However, I still have a battery problem. After I attached the new battery I tried once to power up and check it is working. It booted up OK, but the battery meter said the battery was almost empty. I thought this was a bit strange, since lithium batteries are normally supplied at least 60 or 70% charged. I powered off, and plugged the charger in, but it does not seem to be charging. Has been plugged in for a few hours now and when I try to power it on I just get a blue LED light turn on for a few seconds (you can see it through the connector holes) and then nothing. I haven't seen the battery charging screen even. This is the same behaviour as with the old battery.
With the original battery, if I left it plugged in all night it would try to start booting in the morning, but never finish. I think that there is either something wrong with the charge circuit on my device, or I am simply not providing enough current? I only have 1A USB chargers available, could it be that it just needs more juice?
Update: It powered on again, but only for 5 mins. It doesn't detect a charger at all, tried 3 different ones and many different USB cables. I think this device is toast