You have to send to Sony for repair or you can order the battery and try to open & replace it yourself (of which I have no idea how to get it open). This is the response I got from them:
Thank you for contacting Sony Parts.
Great news! We have located the product(s) you were looking for.x23491021 Battery $98.18
(Shipping charges and local taxes are additional)
You can order the above available items through our website at http://servicesales.sel.sony.com
, or speak with one of our qualified sales specialists (800) 488-7669.
Monday to Friday - 8:00 am to 12 am (Midnight) ET
Saturday and Sunday - 9:00 am to 8:00 pm ET
Also please note that replacement parts do not include installation instructions.
Thank you for choosing Sony.
The Sony Parts and Accessory Team
There is also the option of sending your X in for service but you may not get another X back. They may send you a replacement of the same value. This is the response you get when requesting service for an X:
"Exchange Service Information
Your unit is covered under an exchange program. The exchange is for the same or a comparable model. The replacement unit will be factory recertified/refurbished.
A recertified and/or refurbished unit is one which is not an original, factory fresh unit; for various reasons, it has been returned to Sony from a dealer or customer, or for some reason cannot be sold as "new". The recertified unit would have been through a complete re-work and inspection and, except for possible minor cosmetic flaws, returned to the original factory specifications. It is then repackaged with all of the accessories and supplied materials a new unit comes with, unless specifically otherwise noted.The cost to exchange this unit under our Exchange Program is $204.78 (plus any applicable taxes). Return shipping is included in this price.
This quoted price is based upon the direct replacement model. Product availability and pricing may vary if the direct replacement model is not available. If this applies, You will be contacted by a customer service representative.
Based upon the information you have entered, your unit appears to qualify for the Flat Rate pricing quoted above. Not covered under our Flat Rate pricing is the following:
Units requiring replacement of display devices*
Internal corrosion or moisture damage
Cosmetic parts **
Misuse or excessive wear. ***
Units older than seven (7) years from last market date.
Damage resulting from prior service.
If upon examination, it is determined that your unit does not qualify for Flat Rate pricing, then a parts and/or labor repair quote will be given to you. If you approve your estimate, payment must be made in order to proceed with repair. If you refuse your estimate, you can elect to have your unit disposed at our facility or your unit can be returned to you for a nominal fee. All repaired units will be returned to you with a 90 day part and labor warranty covering the entire unit.
During the course of the repair of your unit, it is possible that data, software or other materials stored or preserved on your unit will be lost or reformatted. It is your responsibility to backup any data, software or any other material. If you are not comfortable with performing this backup process, we suggest that you contact a service professional. Sony does not perform this type of service and will not be responsible for any damage or loss of material."