When I've seen the auction on Ebay, I realized it must be the battery. Well, today I got it, and I was right, sort of.
It was indeed the battery, but that's because the motherboard was fucked up :/
After I opened the screws (which was a huge pain in the ass, as I didn't have an apropriate screwdriver, so I had to use various tools, among which even a drilling machine (really, I am NOT kidding!)..
So anyway, after I opened them I realized that the part of the mb wher ethe charger jack was, was fucked up (burned).
I was like: "Fuck!", but then I measured the voltage for the battery and it was something like 3.1v. Most of the devices using LiIo batteries will not turn on when the voltage is that low, to avoind losing the memory data.
So again, I charged this batter manually, like I did with the last defective PDA I got, and then it powered on just great.
Now, the reacharging the battery with it's normal addapter is out of question, so tomorrow I will drill a small hole in the back of the case and put a few wires there so that I can charge it manually, probably from some solar panels that I have no other use for.
While I am at it, I will probably install Linux on it as well.