I went to Sony's Vaio webpages to see what the multimedia PC has. And I see it's set up for digital video and not analog, darn it.
So digitizing your analog VHS library is going to take more hardware. there are several devices to do this, but deciding which to use depends on exactly what you intend to do with the results.
If you just want to make DVDs quick and easy with no fancy menu effects or video effects, it's hard to beat the new, low cost direct video to DVD stand alone boxes. They're under $300 now at Walmart. But there is a caveat, they will not copy Macrovision copy protected commercially produced VHS tapes. And sometimes home recordings can trip the copy protection filters.
Another route, that's not nearly as easy but should work for all VHS tapes, is to use a Hauppauge PCI bus PVR-250 TV card. It has external video input (composite) that works with VCRs and doesn't react to the Macrovision. It also has a hardware MPEG2 compression chip that takes the load off your PC's processor. The resulting files can then be edited and a little special effects added then used with a DVD authoring program to make the final files needed for a DVD. (You don't want to edit MPEG2 files too much, each edit requires decompressing and recompressing and adds a lot of distortion each time.)
Last, and probably the most appropriate for your computer, is an external video to firewire/DV converter, like Canopus' ADVC100. This will let you use the DV software that came with the Vaio to do all the editing and authoring.
POST EDIT ---
I rechecked their webite and eventually followed a bunch of different links that led to something called the 'Giga Pocket® Personal Video Recorder' that is available for the Vaio. It comes with hardware and software. See if you can find that software on your Vaio. If it's there, then that's what to use.
Fav quote - "Experience is whatcha don't get 'till ya don't need it no more."
System - Athlon 1.4GHz, Win98, Hauppauge PVR250 receiver and compressor.
Software -Magix Movie Edit Pro 10, Nero 6 + NeroVision Express, Moho 4.61, PSP 8.1, Bryce, Quicktime 6.52 pro, Goldwave 5, DVD-Lab.
Cameras - Panasonic GS9, Canon ES8400V, Canon EOS D20 and Canon A70