Chosen Solution

Is there any chance to fix or replace the brown connector of the brand new battery that I had bought for my Ipod?

brindecfe, it is an SMD connector and possibly can be resoldered. If you have all the parts to it, take it to a place that does SMD repair (most TV repair placed do it know), unless you have the tools and the experience to do it yourself. If you lost the connector it is available at places like this. Also read this question The Brown connector broken.. You are not the only one….:) Hope this helps, good luck.