Sorry if I have missed it - but I can't seem to find a post with the same problem.
I've bought 4 of these XPS 12's now and this is the only 1 with the problem.

This laptop was initially experiencing many problems, including this problem. It was eventually diagnosed with faulty memory. So motherboard has just been replaced which fixed all the other issues except this.

If laptop is turned on – and I plug the charger in – the screen brightens – but everything freezes - mouse keyboard everything – and it doesn't indicate it is charging - if I unplug the charger it immediately un-freezes.
Sometimes if I remove the charger – then plug it back in – problem is resolved.
Other times that doesn't work – so I remove the charger and shut it down – then restart it and problem is resolved.
If I start the laptop with the charger plugged in I never have the problem.
It is not happening every time at the moment – but it was happening every time until I recently had the motherboard replaced due to faulty memory - I watched the tech do this but can't remember now if the charging port is part of the motherboard or part of the chassis? - if it was part of the chassis I could see how this could be where the fault lies.

I have tried it with 2 different genuine dell chargers but the same problem.
The bios recognises both chargers.

I have also upgraded from Windows 8 to Windows 10 with no improvement.

And I upgraded the bios to the latest A08 with no improvement.

I intend to contact Dell support again to troubleshoot this. However this is a friends laptop and they use it for business purposes so I will have to take time off my work to go to his work and then phone Dell from there. So I was trying to narrow down the possible causes as much as possible before I contact Dell. My gut feel would say it is a motherboard issue. But the chances of 2 separate motherboards having the same problem seems unlikely. Same thing with the chargers. Thanks for any assistance. I love these little laptops but they seem to have their issues :(