If your PSU features removable cables, ensure they're firmly attached at both ends of the component. Motherboard and PSU.
Could you describe how you transported the PC? I've transported a desktop once in a wheelie suitcase. I ensured it was well-padded on all sides with blankets. Even still, I was cautious and gentle when traversing rough surfaces.
If you have an Integrated Graphics Port (DVI or HDMI port on the Motherboard itself) then try booting your system with only the CPU, CPU Cooling Unit, 1 stick of RAM and PSU attached. Ensure the Monitor is attached to the Motherboard, or that you have installed and attached the Monitor to the Graphics Card if no Motherboard Monitor connector is present. Make sure Graphics Card is removed from the system if the Monitor has a graphics port.
You could closely inspect the Motherboard for any damage or loose components. Compare the Motherboard to an image of your exact Motherboard model number (you can locate the image on Google or a similar search engine easily).
Before undergoing the RMA process you could try a complete dismantle and reassembly of the PC. That will rule out any overlooked connections or components that may have come loose.