Help me narrow down a problem.

Greetings from India!

My iPad was working fine and one day it just went "off". It had low battery and I tried restarting it by following the procedure mentioned in the forums. And yet it refused to start.

Post trying to press hold power and home button for more that 1 day, the ipad started and it shows home screen with 100% battery but, the moment I take it off the power supply it switches off.

Also when I connect it to the wall socket, it shows low battery at first then 2 seconds later it shows 100% and i'm given access to the homescreen with a message which says, "connect to itunes".

However, I cannot connect to itunes as I can't do so without taking off the wall socket and it wont start when i connect it to my mac(tried for a day continuously too)

I seriously don't know what the problem is and how to fix it. I had taken my device to the icare and they said they can't open the device(company policies) and I have to get a replacement(which costs me more than the ipad value itself ie 25000 INR, where as the new costs 20000 INR)

Is there anyone out here, who can suggest me what and where it could have gone wrong, so that i can try fixing it by myself?

Thanks in advance.