I called UK Customer Service 0800-587-1456 who initially tried to convince me that it was out of warranty (18 months) but when I insisted that I wanted it fixed under the UK's Consumer Rights Act 2015 I was transferred to the "Out of Warranty" team. After giving them my Service Tag and emphasising that the touch pad was raised they admitted that there was an issue with some batteries. In my case they replaced the battery, palm rest, touch pad, and keyboard.
Hi, I have exactly the same problem on my XPS 9333 which is also out of warranty. My laptop was bought in the US but I'm living now in Europe. Entering my service tag gives me the only option to call to the US number. Do you know if there is a good way to contact them, e.g. in writting? Even if I wanted to buy and replace the battery myself, I'd need at least the part number. But I'm unable to find it and afraid of buying a fake item and enter in a bigger danger than it already is with the swollen battery. Thanks.