My first question would be what was the last thing you did to the computer :)
Sometimes it is just a miss mach of screen resolution so try:
Resetting an out-of-range resolution
If you set a resolution inappropriate for your monitor in the Screen Resolution GUI tool, you can reset it from a terminal by running
$ rm ~/.config/monitors.xm
Alternatively you could:
Use the VAIO Hardware Diagnostics utility to diagnose hardware issues using the VAIO Care™ software.
http://www.kb.sony.com/selfservice/viewContent.do?externalId=C1013171&mdl=VPCF115FM
That will tell you if you have more serious problem of bad hardware.
How to:
Booting into recovery mode
Switch on your computer
Wait until the BIOS finishes loading (you will probably see a logo of your computer manufacturer)
The following messages may show up:
Grub loading stage1.5
Grub loading, please wait...
Quickly press the Shift key or Escape, which will bring up a boot menu. (If you see the Ubuntu logo, you've missed the point where you can enter the GRUB menu)
Select the line ending with '(recovery mode)', probably the second line, something like:
Ubuntu, kernel 2.6.17-10-generic (recovery mode)
Press enter and your machine will begin the boot process.
After a few moments, your workstation should display a menu with a number of options. One of the options (you may need to scroll down to the bottom of the list) will be "Drop to root shell prompt".