My Sony Vario Laptop running on Windows 8.1 occasionally starts flickering and when I try and input data it only accepts occasionally. How do I troubleshoot this problem?

Does it flicker only within Windows or BIOS also?

Attach Sony Vaio Laptop to an external monitor and check if it does flicker there. If it doesn't it should be caused by the LCD panel it self. If that be the case then you have to contact the authorised technician to get things done. May be a replacement will resolve the issue.

Otherwise:

Update the display card driver to the latest version

You may need to run the display troubleshooting tool by going to Start -> Control Panel -> Troubleshooting -> Appearance and Personalization -> Display Quality

You can also go for a System Restore. Select any restore point when there was no such issue.