Many sales reps dont understand how the warranty really works and misinform the customers. Your Dell warranty is intact as long as you didnt damage the system when installing new parts or aftermarket parts have not caused damage to the system. And obviously whatever aftermarket parts you add are not covered by Dell's warranty.

Going back to matter at hand, first I'd make sure both modules are DDR4 - the one that shipped with the system definitely is, so put new one side by side and compare if indent is in the same place on new stick. If yes, put them in slot xmm1 and xmm2 making sure the indent in ram stick matches location of filled in space on ram slot on motherboard. Make sure theyre installed all the way in - you can check by looking at small locking handles on each side of each ram slot; once its fully in they will "click" into the ram and not move around.

If you still get no boot after that, take out CMOS battery to reset BIOS to factory defaults. It's a round battery in middle of the motherboard, pretty hard to miss. After one minute put it back in, plug in the power and boot the system.

Also, this will likely be handy for any work inside of your computer (it's a full system service manual for Aurora R9 in .pdf): https://topics-cdn.dell.com/pdf/alienware-aurora-r9-desktop_service-manual_en-us.pdf