so of what I looked up and read from a previous post on here saying that it needs a battery replacement. I also read that just trying to unplug the battery connector then plug it back in and retry the restore it may work. They did do it on a iPhone 4S though so it could be different. I hope I could help and I hope you find out how to fix the problem.
Well there could be a few problems. Your phones battery could be dead if the battery is dead it wouldn't connect to any computer as it wouldn't be getting a charge to do anything with. That seems more like the problem in my opinion. Your charging port could be broken also which would say why it isn't connecting. You could also try hard resetting your iPhone first.
Contact the support of the website. They have a lifetime guarantee if the part itself is defective, but if it isn't they will charge a 15% or $5 for restock. So make sure it is the part defective and not your IPhone 4s. That's all I know how to help. Hope you get your problems worked out never stop repairing.