Phone keeps turning on and back off. What do I do? This morning, I turned on my mobile, which had been fully charged during the night. It displayed the usual white «Samsung Galaxy SIII Neo  powered by android» thing, but then it vanished, then it reappeared, and it has been doing this throughout the day, for all I know. I tried googling, and found out about:


FastBoot, which is acheived by pressing Vol+,Vol-,Power all at once; this does nothing at all on my device;
Recovery boot, which is acheived by pressing Vol+,Power,Home all at once; this displays a small blue «RECOVERY BOOTING…» on the top-left corner, but only if the phone is connected to a charger, otherwise nothing happens;
Hard Reset, but this seems to be impossible, as it requires (see here) the phone to be completely off, which is, at present, simply impossible.


Removing the battery won't do anything: I tried that several times, but as soon as I put it back, it goes back to doing the above. Also, connecting to the charger makes the «Samsung Galaxy [etc]» display like 2 or 3 times longer.

What should I do about this? What is wrong with my phone?

Update

Following @MatthewRead's comment, I tried Vol-,Power,Home. Something flashed on the screen, and then back to on-off-on-off. This is a frame of a short movie I captured with another mobile:



Sorry for the name of the movie showing up and hiding «Warning». I just tried Vol+ as that screen suggests, and now the screen shows up no more. One thing is sure: holding down that combination now stops it from on-off-on-off-ing, but as soon as I release, we're back there.

Update 2

I tried other key combinations, and this is what I found out:


Vol+ -> Recovery booting;
Vol+,Home -> Recovery booting;
Vol+,Power -> Recovery booting;
Vol+,Power,Home -> Recovery booting;
Power,Vol- -> screen above;
Vol-,Home -> screen above;
Vol-,Power,Home -> screen above;
Vol- -> screen above.


The last two have not always happened, but maybe I thought I was pressing when I actually wasn't. The screen says to hit Vol+ or Vol-, but none of those does anything.

Update 3

Someone suggested I scrape the battery contacts, I did it, and now the mobile seems to be working again. So this apparently saved me the trouble of flashing, though I have the firmware downloaded in case something goes wrong.
Try this take out your battery
Wait for 10 seconds
Re Insert the battery without pressing the power button 
if it turns on itself (witout pressing the power button( then it would be hardware problem. Just clean it with alcohol or tinner and keep pressing on it to clean the inside of your power swith or if not just replace your power button. 
If not auto turn on after inserting the battery then its software problem. Just download the official firmware ang flash your phone via odin.