If you don't see anything when turning on the system at all that would likely be a failed supply. For seeing fans and drive lights come on a for a few seconds and then everything goes dark that could well point at a board problem.
A bad dimm would likely see blue screens just when Windows was first loading. But since that is a brand new build it's likely a component failure since you were running it for 3 weeks straight without noticible memory problems. On the build here the first board ran good for 3days and then took a permanent vacation.
When pressing the power button fans, drive lights would all startup and then everything instantly shutoff in about 2-3 seconds. If you are seeing something like that you won't be able to run memtest since that needs several hours to repeatedly go through the series of stress tests it places on memory.