I really doubt there's a way to boot from PCMCIA cards - but have a look at the BIOS, maybe there's an option. Does that specific Vaio model have a CD drive? If so - there are also bootable CDs, so that might work, too.
With the old Apple laptops, it was possible to pop in a SCSI cable between PC and laptop, and the PC would treat the internal drive of the laptop like any other SCSI HD. That was pretty cool, one of those neat Apple things. I don't know if there's any way to do the same with PCs, or even modern Apple laptops.
If all else fails, you'll have to open the laptop and remove the 2.5" HD and install it into the PC. I am not sure, but from what techhead said it seems as if the cable would be different from the standard IDE cable, so you'll need the adapter he talked about.
Good luck!