Boot loop, help needed

Hi,

I've had my Nexus 6 64Gb for about two and a half years now, and it's mostly served me very well. It's quite slowed down now, and the battery has really weakened, but when it's charged it's working mostly ok.

Unfortunately, today, the battery run down completely, and the phone shut down. I don't know if this has happened maybe once or twice ever since I've owned the phone, but it was never an issue before.

Now, I can't get the phone to power up. :(

I've plugged it into a charger and it shows the battery being charged symbol in the middle of the screen. If I attempt to power it up, the white Google logo and an unlocked padlock show up on a black screen for about 2-3 seconds, then the screen goes completely off, then 2-5 seconds later Google logo and the padlock show again, for a few seconds, and it just keeps going on like that. I don't even get the coloured Google dots.

I can get into the bootloader (I think that's the right term), by holding the power and volume down button. I tried wiping the cache partition, and it does this, but it doesn't help and I still can't power up the phone.

Is there anything I can do that ISN'T a factory reset? I'd like to preserve the data on the phone and not have to go through hours and hours of complicated process of fully resetting/flashing the phone and having to reinstall everything.

I realise it may not be possible to avoid having to factory reset the phone, but I'm really hoping there are other things I can try before resorting to that.

I'm fairly technically minded and PC literate, but haven't done much "advanced" stuff on the phones... I have once in the past flashed the phone and I think that's when I unlocked the bootloader (I'm really not sure I'm using all the right terminology here), but like I said, I'd really rather avoid doing all that again, if at all possible.

For info, about 3-4 weeks ago I finally got the OTA update to 7.1.1 (from 7.0) and I did that and it all went smoothly and the phone worked fine, until this happened today.

Many thanks, really appreciate all advice and help given.