moto g2 caught in restart loop this is a year old phone just barely past the warranty,its running on kitkat 4.4.4 with no rooting or any other tweaking with system.

a few weeks ago i left it at night with google music playing and the next morning i found it caught in restart loop. it was constantly restarting and i could not power it off. it would light up and goto the moto logo and with a vibration go off and repeat this. earlier the frequency of restarting was very high now it has slowed. also the battery shows 0% and low in boot menu but turns ok on charging for some time.

only thing i can do is get into flash boot menu and when i select normal or recovery the phone restarts and again goes blank. it gets warm when charging or when its restarting.moto care has asked to take it to their centre but theres none within a 100km radius

now its been around three weeks, ive found no solution for this other than factory reset which will delete all my data on the phone to make it usable again
i dont want to lose my stuff as there are many imp pics and notes etc 

is there any way to save my phone without formatting the data or can i recover the images and other files once factory setting are restored?
im not sure if i had synced or made any backups

there were two changes i made before it all happened
1.the phone was out of space i moved watsapp videos to my pc and freed around 2gb
2. that night i installed adobe flash player from a movie site

pls help me guys im just a naive user and dont know any programming etc
One way that might be possible is to connect your phone to the computer using usb. I'm not sure in kitkat but you can then safely transfer your most needed files to the computer. You may need to have usb debugging options enabled however.

Also, if you have a removable case then do it and remove the sim card (and the battery if you can). I had a similar problem and the phone fixed itself after removing the sim card.

Most cases are specific to the phone and most likely hardware based. If you can find a repair center near you (doesn't have to be moto care but make sure it is a licensed repair center) they could probably pinpoint the problem.

Hopefully you will be able to fix this issue.

I have linked some websites below that may be useful:
http://forums.androidcentral.com/ask-question/418757-moto-g-stuck-boot-loop.html
http://www.droidviews.com/how-to-recover-when-your-android-device-is-caught-in-bootloop/