Had the same problem and found myself a solution for my Sony Vaio PCG-71811m.
I thought that the solution is to take out the BIOS battery so I needed to open it.
Found a tutorial that helped me to open it here
https://www.ifixit.com/Guide/Sony+VAIO+PCG-71811M+Heat+Sink+Replacement/33927 .
You will probably find one for your specific Vaio.
And YES, at least in my case, it's working again!
So open it, remove the BIOS battery, wait about one minute, put the battery back, and enjoy!