Hi,
What was the amount of old RAM installed and do you still have the old RAM modules?
''If 4GB of RAM was initially installed'', the top slot was most probably empty and never used, is this correct?
With the battery disconnected (see below) visually inspect the top RAM slot for any damage etc. use a strong light and a magnifying glass. You could also try ''gently'' cleaning the top slot contacts with a Q-Tip lightly (very lightly) moistened with Isopropyl Alcohol 99.9% (available at electronics parts stores) to see if this resolves the problem.
''If 6GB (4+2) was initially installed'', does it still work when you reinstall it?
Are the 2 new 4GB RAM modules (or did you only get 1?) identical as to frequency and latency etc i.e. exact same specifications?
Did you disconnect the battery from the laptop when you removed/replaced the RAM modules?
Here's a link to the [https://downloads.dell.com/manuals/all-products/esuprt_laptop/esuprt_alienware_laptops/alienware-m14x-r2_owner%27s%20manual_en-us.pdf|service manual]. On p.29 it details the pre-requisite steps (showing that the battery needs to be disconnected) and then the procedure to use when removing the memory.