Try unplugging it from power for a couple of minutes. Also make sure the power cable has been fully inserted into the Beam. If this doesn’t work, contact Sonos Support:

https://support.sonos.com/en-us/contact

If you are having trouble getting the power connection fully seated a light touch of dry silicone lube can make it easier to seat.

Do not use a wet or grease based lube.

I have given it up as a lost cause.

So, what did Support say, when you called in as suggested by @GuitarSuperstar ?

I called support and tried to explain my problem, unfortunately neither of us was able to understand the other.

I should add that this problem is only the most recent in a long list of frustrations I have had with Sonos products, I own three, the Beam, a Play3 and a play one. At present only the Play 3 is working.

Why were you unable to understand them? I’m assuming you were both speaking English, no?

Ah, I see he provided the US contact, perhaps this link will get you to a more local support person: Sonos Support

If I were to guess, the most common issue that people have with Sonos tends to be down to network issues, although that certainly wouldn’t be the case with a device not powering up.
 

That, unfortunately, is something this community where you’ve posted really can’t help, other than, as you’ve seen, suggesting reseating the power cord, or checking the fuse for the mains where it’s plugged in. Hardware issues ultimately need to be discussed directly with Sonos. 

It seems strange your explanation of the Beam not powering up would not be understood by a Sonos representative. What happened?

For your other problems: just mentioning your problems does not help anyone. Can you explain your problems?