Best of Luck ! Tip : Don't buy an adapter. Take it to a store which sells genuine adapters  Test, if it works than pay.  Else Next step would be to get Motherboard replaced.     
My 3-year old XPS 9560 suddently became very problematic over the last few days. I have always kept good care of my computers/laptops so the laptop was running great up until Sunday (3 days ago now). When I turned the laptop on that morning I got an error saying "The AC power adaptor type cannot be determined. Your system will operate slower and battery will not charge", etc. I think this error has come up often with these laptops going by online searches. Anyway, I hit the continue button thinking I would look at the issue properly a little later. I had a short job to do then shut down the laptop. Later in the day I came back to the laptop and could not turn it on. When I pressed the power button the system would start to power up but after 2-3 seconds would just shut off, as if I tried to start it with a dying battery. However, I had the AC adapter plugged in so I was expecting that it would start off the AC power and not the battery. If I unplugged the AC adapter from the DC jack it would not power up at all.  Because I was desperate to get to work with some upcoming college assignment deadlines I had to try something. I removed the battery and attempted to power up the laptop from the AC adapter with the battery disconnected. This worked in that I could power up the laptop without any problems. But when I re-connected the battery later on I had the same problems I mentioned above. Since then I have left the battery disconnected so I can get some work done, but now my laptop is very sluggish. Simple tasks like opening a web page can take minutes to carry out at times. The CPU seems to max out at 24% and flatlines here on the CPU % Utilization graph in the Performance tab of the Task Manager. Has anyone else had the same problem and found a way to get around it? I have seen some posts suggest various tricks on holding the power button for a certain period of time, etc., but no of these have worked with the battery connected. I have seen one case suggesting a DC jack replacement but the DC jack seems fine to me, there is no movement in it and power runs perfectly into the laptop. The battery appears visually fine with no obvious swelling or anything else and I had no sign of its condition deteriorating beforehand as it held power fine until the weekend. I also cannot run any diagnostics or do anything else with the battery connected because I have not been able to power up the laptop to try or test anything when the battery is connected. This is really frustrating for what was an expensive purchase. Having spent the money to gain the benefit of performance it promised I now have a laptop where performance is a bit of a joke...
XPS 15 9560 sluggish following AC adapter/battery problem