Battery fast discharging and doesn't charge any more

Since several days my Samsung Galaxy S2 has presented an anomalous discharching behaviour: once fully charged, it discharged linearly from 100% to about 45%, then the battery level jumped down to about 15% and the battery completely discharged in few minutes.

Last night, I charged my phone for the whole night but the battery didn't charge any more and now it is completely discharged and the phone does not turn on.

I think the battery has dead, but I would like to be sure before ordering a new one; do you suggest any test to do? I read about the excessive discharging protection, how could I reset it?

Thanks

Francesco