LG KS360 battery problem?

Hello,
I am using a LG KS360 mobile phone at the moment. A few months ago my battery died..it was a LGIP-330GP. I decided to replace it by a new one but i could not find a LGIP-330GP so i got a LGIP-411a as it was the same. but the mobile after using for a while just shut down at random and i cant turn it back on unless i plug it to the charger and then turn it on, then remove the charger. It is embarassing for when i go to college and when i do not have my charger with me. I wonder if this could be a battery problem? Also i noticed that the mAh of the 330GP is 800 and the mAh of the 411a is 750 . Can you help me on this?, thank you