You need a REPAIR install disk so that the system can get files from it. A factory restore means that it basically deletes the main partition and uses information from the hidden partition to re-install but that doesn't mean that install files are kept in that hidden partition. You should have made one (REPAIR DISK) yourself prior to the reset, the instructions would have been in the Start Menu > Maintenance section.
You will need a Sony Vaio REPAIR OS disk which you might get from Sony but may have to pay for it.
If, per chance, you do have a repair disk, you have to change the boot sequence in bios to the cd/dvd drive as primary then insert your disk and boot to the disk and follow the repair/restore instructions.
It is never a good idea to restore a laptop especially a Sony Vao as they use proprietory drivers that are not readily available even from Sony.
You will have to contact Sony Vaio website directly to acquire drivers for the laptop, citing your make and model number.