I suggest that you charge your phone for a couple of hours using the wall charger, then try to start the phone by press and hold the power button and volume up at the same time. You could also try to remove SIM card and SD card from the phone and try to boot the phone without the card inserted.
If you still can't start the phone, try to repair the phone software using PC Companion:
http://www.sonymobile.com/update
In PC Companion, press start on Support Zone > Start on Update the phones software > Press the blue link that says "Repair phone". Do this without the phone connected and follow the instructions in the program.
