My Acer One ZG5 was not charging for the last year or so. I took it for repair to my local friendly and trusted Wizard Electronics but the chap there was too wise. Armed with the knowledge that it failed to charge two different batteries but yet would boot up under charger power he could conclude quite well that it was not the charger, the connector or the batteries and some troubleshooting on the system board was required. I already knew this of course which was why I took it to him; but he suggested it would be cheaper to replace the main board and a quick look at ebay prices for smashed screen netbooks showed that he was right.
However, to my surprise, while googling to find what the motherboard fault might be I found a clue that it might be (and was!) fixed with a BIOS update! http://www.acer.com/worldwide/support/download.htm and one version 3110 release later and I was charging both batteries again!