Losing date and time may very well indicate that the CMOS battery is failing. Not too sure about it powering up once mains power is connected – this may possibly be a separate problem.
Replacing the CMOS battery is not a simple task as it requires disassembly. And unless you feel comfortable with this I suggest that you contact one of the Sony repair partners or a competent local repairer.
As an alternative to changing the CMOS battery, if your system is always connected to the internet, i would suggest you to use software like BetaClock (which also offers a customizable tray clock display) or Neutron.