Dell XPS 13 9343 intermittent boot failure

Hey everyone! I'm new to this forum, but I am totally lost on this issue.

I have an early 2015 Dell XPS 13 9343, i5 with QHD+ touch display. I have been experiencing an intermittent issue where the system doesn't boot or even display the Dell logo, but gives a series of 3 slow, foreboding low-pitched beeps at about 3 or 4-second intervals, followed by a higher-pitched beep after which the fan revs and the system powers off. The front indicator light quickly and repeated flashes 3 amber followed by 1 white. 

According to the guide at http://www.dell.com/support/article/us/en/19/sln295543/how-to-use-and-troubleshoot-the-xps-13--9343-?lang=en, the beep code indicates a system board failure, the common remedy of which is to replace the motherboard. What mystifies me is why this issue only occurs intermittently. For example, I am typing this post on my XPS 13 at the moment, and everything is functioning perfectly smoothly. But I could literally close the laptop, go get coffee, come back, and it would be totally inoperable. In the same way, earlier today I tried to show a friend at school how it wouldn't boot, and it woke up in 6 seconds as if nothing had ever happened even though it was making alien spaceship noises no more than 5 minutes earlier.

This problem has been haunting me since this spring. It happened several times with the same symptoms, and I ran a BIOS update (when it happened to be working) and the problem disappeared, only to return again this morning. It has gone back and forth from totally working to completely inoperable several times in the last day.

I rely on my computer to take notes during class, and though I have everything backed up on OneDrive, it would be killer to open it up simply to broadcast spaceship noises to the entire classroom.

This is a long and drawn-out explanation, but hopefully some of you smart people can make sense of it.

Cheers!