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hmmm... I'm no VAIO Expert, but i think you can put ANY dvdburner into your computer... but wait for the answers of others, because i don't know much about burners or VAIOs.
Ice_Lane is correct - you should be able to fit any EIDE writer. I would suggest one of the 4 speed dual format drives.
I suggest that Sony one which you can do every format except DVD-RAM, it's a good all rounder.