rebuild after water dammage

Stephane, lets start with this question that you have "and why when i plug the ipod on wall charger its start but not recognize by Pc ????" This is because of a water damaged battery. Your AC charger supplies a higher amperage than your computer. " and if i plug the ipod on a wall charger it power on (still no backlight) i could listen to music with earbud and if i leave it there the charging battery logo appears (like normal ipod do) but as soon i unplugged every thing turn off (like no battery power)" same reason here. The very first thing I would suggest is that you clean the iPod thoroughly. Rice is a great first aid, but it will not clean the logic board nor will it prevent corrosion. The iPod Nano is a bit of a PITA to work on. Use this guide to remove the logic board. Clean it and all connectors and cable ends with a high grade isopropyl alcohol (greater than 90%) Be very thorough with this, but also very careful, you do not want to knock small components of the board. Yes, it is okay to submerge it in alcohol. Once you are absolutely sure you have it cleaned, again, I can not stress the importance of this enough, replace the battery. You can use this guide as a supplement to the first on. The big problem here, besides the finicky work, will be the backlight. It is possible that it is your LCD that needs to be replaced, since it contains the backlight. It may also be possible that it is the backlight coil on the logic board, it acts as a switch for the light. I would order a new LCD just to be on the safe side, and it is easier to replace than the parts on the logic board. Parts are available right here. Hope this helps, good luck.

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I attached an image of one one the iPod 4 logic boards. It does show the location of two coils. One of those is the backlight coil. Check for continuity, if it does not show continuity, replace it. You could try a 6R8 or may be a 4R7. Check with places like digikey.com or mouser.com. They do list the sizes of their coils. As you can see, the coils are very small (approx. 2mm), and extremely difficult to solder, unless you have the experience and the tools.