Viao Clock and Calendar broken

I've read a few conversations regarding similar symptoms, and tried all the suggested solutions, with no success. The laptop keeps proper time while on, but stops keeping time when I shut it off. I replaced the CMOS battery, reset the bios to default, manually reset the time in bios, changed the time zone (it worked for someone...), but no go. 

I'd just ignore it, but certain websites won't work if your computer's clock is too far off.

This Vaio is Model # VPCF23EFX, upgraded to Win 7 Ultimate. 

Thanks in advance for any suggestions!