Share your experience!
Are you using the phone while charging?
what if you try something basic and restart the phone ?
It'll be wise to repair the phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
boot on safe mode and check again
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
Hi Rmcspurs, welcome to the community 
here are some further steps on running the repair:
Running the software repair on PC Companion:
1. Install and open PC Companion then select Support Zone.
2. Phone Software Update.
3. Start.
4. Repair Phone
5. Continue
6. Accept data removal
7. Next
8. Wait for prepare
9. Select Phone
10. Follow the connection steps
Running the software repair on Bridge for Mac:
1. Launch Bridge for MAC without the handset connected.
2. On the Main Window select "Xperia > Repair Xperia
Device".
3. Ensure the phone is charged and select "Ok" in the
following window.
4. Select Continue on the following page.
5. Wait until the initialising step is finished the
continue as below.
6 . Select your model of phone from the list that appears
7. Follow the connection steps that appear, ensuring that
you are holding the relevant button down before during and
after the connection phase until the update/repair begins.
Hi RMC Spurs
I have the same problem for months now, not able to charge at all when off and battery jumping up and down on display.
Can you tell me what exactly you did with the back to fix it please? )