If you get no atomiser error then it's likely there's no connection from the 510 pin to the coil. Either the pin isn't making contact with the battery supply or there's a break inside at some point due to a manufacturing defect.
If you want you can extract the liquid from the dud cart to put in a new cart. I believe you can buy new carts on Ebay for like a couple pounds each, Liberty V9 I think? Or at least something similar. Probably want a new one as used ones you have will be gummed up.
The liquid is quite thick but if you (gently) heat the dud cart the heat would make it flow better, then use a thin syringe to extract it and move as much as you can to the new cart.