Not sure about the battery being the cause: I would have thought that, even with a dead battery, the phone would start if it was plugged in. Of course, I could be wrong (and I kinda hope I am as this would not be good news).

Is the phone still under warranty? If you're in Europe all phones have a 2 year warranty so you might just sneak in under the wire.

 

My nexus 5X had the dreaded Start Up Loop issue. It was out of warranty, but I sent it to LG and they repaired the device and sent it back to me. A very good experience with LG; great service and communication.

However, after running the provisioning process and Android update it died again. Freezes on Boot Up and garbled screens.

LG once again said "send it back". Prepaid shipping too. We'll see if it can come back from the dead.

My old Nexus 5 is my backup running under Project Fi; some what limited function and frequent visits to the charging station, but it's serviceable.

 

I had exactly the same thing happen to my 5X on Friday. The screen suddenly froze, the phone died and then wouldn't respond to anything, including debug mode.

Fortunately, I'm in europe so despite getting my phone within days of it's release, I still have around 6 weeks to run on my regulatory 2 year warranty. I spent around 30 mins on-line with a very pleasant guy from Google support Friday evening and Monday afternoon, my replacement arrived. Earlier today I got notification that my old phone was delivered to Google so I'm now waiting for them to confirm that the phone wasn't water damaged or whatever else might invalidate the warranty.

The replacement phone is a refurb but looks and feels like new. Only difference is that it's the black version when I had the white - turns out I prefer the black Plus it makes it seem like I have a whole new phone