Galaxy Nexus i9250 battery charging problem.

Hey everyone. I have huge problem with my Galaxy Nexus i9250 for few days now.
Let me start from beggining.
First it was showing charging symbol even if it ain't plugged in. Then it stopped after I cleaned charging port.
Few weeks back there were great floods in my region (Bosnia) and we were in lack of electricity so I started to charge it on a car charger and after it's completely charged (2h) as soon as I start to use it the battery goes off really fast, example, if I use it for let's say calls or even on "stand by" after 30mins the battery goes for like 40%. That's when problems started to begin. If it was turned off becuase of lack of battery I had to turn it on by pressing "Down volume + power" for first 2 times. Then I had to remove battery for few seconds then put it back not completely but I had to press the battery against those 4 pins which conduct electricity to a cell phone and press those two buttons for like 30 seconds to turn it on. Few days ago, I had same problem, but this time it wasnt empty on battery, it was in my pocked with almost 50% of battery when I took it and I saw it was off. Tried again that same proccedure, it turned on, showed recovery menu and it turned off. Ever since I can't turn it on, it charges, but it doesn't show charging indicator on my screen. When I put my battery in other phone it shows it's fully charged. I can't turn it on, my PC won't reconize it, let's say it's dead. I don't know what's happening, so I'm asking here if anyone knows what to do. Thanks to all.

— modified on Jun 3, 2014, 5:27:38 PM by moderator

I tried what you've said and yes, it spins. It may be the funny thing but often people lick battery connectors to see if there's electricity and yes, there is. I don't know what's the problem. I would love to enter recovery and clear the cache but my phone won't turn on. PC doesn't want to recognize it or anything. It's dead. When I put my battery inside Galaxy S2 for instance (Yes it's possible you just need to press it to those connectors) it turns it on, and shows battery is on 89%. Same battery doesnt want to turn on mine. Any other ideas, or I just need to buy new battery? Thank you so much for your time to reply.