Well thanks for the help...

So, i've exhausted the battery and tried to charge it, however the thing is that it still doesn't work:

the apple logo appears: it flashes and, of course disappears, and then the attention-low-battery logo starts flashing until i disconnect the iPod of the bose speakers or the electrical adaptater.

But i noticed that the hard drive don't start running and since i do not have another battery, i can't not test the battery connector.....

So, do you think that my logic board is damaged ?

thanks for answering my post.