I've broken a connector
When you open the iPod, the first connector that you must remove. In the guide it's called brown connector.
There's any way to repair it?
Did you rip it off the motherboard? If so, you *may* be able to resolder it. But it's a very tricky repair.
I believe that is the headphone/hold switch connector. The iPod might function without that being plugged in, allowing you to use the iPod in a dock with a remote control. It's hard to say what the default signal for the hold switch is- in the 3rd Generation iPod, it was a physical switch. In the 4th, it was a signal received through the headphone jack. If the headphone cable broke, the controls were gone too. I don't know if the 5th generation follows suit to the 4th generation or not.
Yes, it's broken, out of the PCB, the motherboard. When i connect the iPod to the USB charger, appears the LOW BATTERY, CHARGING, but in fact it doen't charge. I think that this cable is from the USB to the battery, the cable that charges. I am not sure if i could resold because it's so a small connector. I think that i must give the iPod to an specially shop or something like that.
Ok, here my contribution.
After getting the message "Please Wait -Very Low Battery." I wanted to replace the battery of my iPod Video 5th 30GB, I broke the battery "brown connector" (it was already damaged, hence the message). It was completely ripped off of the PCB, the motherboard, including the solder paths! I could see some very small cupper dots. From these points I started with a multimeter with the Beeping (continuity test) function to trace the paths of the connections, since I couldn't find any diagram schematics on the internet. There are 5 pins, I labeled them for myself by numbers (1,2,3,4 and 5). By measuring I found that there are actually only 3 "main" pins, 1-2, 3 and 4-5. I soldered these points to the battery connector and hot glued it back to the PCB. And now it's working!