Since it's a 2nd gen shuffle (also for 1st gen), you can try using the iPod Reset Utility.
It's only for those two shuffle models, and if you use a Mac or Windows XP (or earlier). It does something like a Restore in iTunes, but works in situations when there is no hardware problem, but iTunes does not recognize it for some reason.
However, I think the problem may be the connection point (the dual-purpose headphones jack), or possiby the cable. It has different connection points for power and for data. So, it can still charge while not working properly as a data connection.
The three parts of the connection are the shuffle itself, the USB port on computer, and the docking cable. The cable needs to be the one that came with that shuffle model, with a mini-dock at the iPod end. The one for 3rd or 4th gen shuffle will not work, because the connector is different (I don't think it will even charge). You can get third-party replacements, but make sure it is described as being for the 2nd gen shuffle.
I'm sure you've ruled out the USB port on computer being bad by trying something else on the port, preferably something similar to a shuffle, such as a USB flash drive. If you can rule out the docking cable, by trying that cable with another shuffle, or by trying a different cable that is known to work, then the problem is likely to be the shuffle's connection point.
thank you for you reply.
I wish I could try the reset utility, but the computer do not recognize the iPod. I installed the program but when I open I cannot click in the button to start the process because the computed do not recognize any device.
I also bought a new cable to try. but nothing, something.
any other ideas?
I'm almost buying another one =(, the problem is that I live in Brazil and believe or not here is about 150 dollars a new shuffle I really don't want to spend this money.
You've ruled out the other possibilities, so the problem must be in the shuffle's hardware.
If you are good a such things, there are online guides for do-it-yourself repair, such as this well-illustrated example
In your case, if you can find a used broken shuffle that is described as not holding a charge (bad battery), you may be able to swap parts to make one that works. Shuffles are not that complicated, but they are very small.