do you know anyone that uses a Sony Erricson Xperia X10 phone? If yes, borrow the battery and test it with your phone. If your phone turns on with the borrowed battery, then this confirms that it's a charging problem.
Read my tip on the below link, to diagnose and solve the problem.
Click here: http://www1.fixya.com/support/r8742993-phone_charge
If the contents in the above link doesn't help, please let me know for further assistance.