NVIDIA Graphics Card not being recognised on Alienware M17x R4 Laptop

This is a strange problem that has been exhausting me (as well as the Nvidia and Dell technical support)

My alienware M17x R4 laptop has recently stopped recognising the NVIDIA GeForce GTX 675M driver. In device manager it can be seen when I show hidden items.

However, I have recently discovered that it shows when I start the laptop running on battery power. On battery power it also shows it being fully updated. When i plug it into the AC adaptor it goes to the blue windows error screen and then restarts - after which the driver no longer shows in device manager.

This started happening after the latest windows update however, I'm not convinced that it is directly causing this issue.

Things I have tried to far are:

• 
  trying to reinstall the driver (cannot detect the hardware so won't reinstall);
  system restore then trying to reinstall driver;
  removing all traces of nvidia and trying to reinstall;
  resetting the PC;
  taking the battery pack out and back in;

All of which have not worked. The only thing that has worked has been to start the laptop in battery power and reinstall the driver entirely on battery power. However, as said earlier, plugging in the AC adaptor leads to a crash-restart.

I read that a similar problem was solved by reinstalling the Dell On Screen Display Driver however, it won't let me do that either.

Operating system is Window 10 Pro

Update: I have tried using another AC Adaptor but it doesn't work. Furthmore, after turning it on with battery power only I went to device manager to see that the driver had an alert/hazard symbol. I tried to update it but it was the latest driver. I scanned for hardware changes and the whole driver disappeared...... So I'm guessing it may not entirely be to do with the AC adaptor.