Why my phone won't charge

For the last 3 months my battery would drain quite fast. Then it got to the point that it would randomly even charge. I replaced the battery last week. The battery finally got a charge of 80% but never 100%. For 24 hours the phone worked perfect. I plugged it in to charge and now I can not even get the home screen to come on!!! There is no response to turning it off and on - NOTHING. This happened just because I plugged in the charging cable. I had 50% battery left at that point (when I plugged it in) so I know it was not a drained battery causing the problem. Any suggestions on where to go from here. Also this phone has been so well cared for. Always contained in a purse or on my desk. It has never been abused.