Hi,
Does the laptop show that it is charging when the adapter is connected?
What happens, if anything when you try to turn it on e.g. fans on, lights if any, on keyboard etc?
Try what is known as a ''flea power release'' and check if that resolves the problem.
Here’s the [https://dl.dell.com/topicspdf/alienware-15-r4_service-manual_en-us.pdf|service manual] for the laptop. Go to p.87 to see the procedure. Basically it entails disconnecting the power adapter if connected and then removing the base cover and disconnecting the battery cable and then holding the laptop’s Power button operated for 5-10 seconds to drain any residual power from the laptop.
Reverse the procedure and then try to start the laptop.
This will restore the laptop BIOS back to its factory default settings in case they were corrupted and preventing a normal start