Wow! Interesting thread here. You mention your Vaio has 2 hard drives inside; I've never seen that one before. But, to your problem at hand.
First I could use some more information. What brands and models are your 2 hard drives?
Next, there are 2 versions of Vista Home; Vista Home Basic and Vista Home Premium. Which one do you have? This is a follow-up to Saltgrass's suggestion of using Remote Desktop to access your hard drive(s). Actually, neither of these will work, as the Remote Desktop option will only work with Vista Professional, Ultimate, or Business versions. Good idea nonetheless.
Do you have another laptop drive available to you to use for testing the laptop that you know for sure works? If you have one to test from a friend or local computer geek that would tell you a great deal. If your laptop BIOS sees the test hard drive *and you only need it go be 60GB or larger for Vista* and you can reinstall Vista from your original or created Factory Restore Discs your Motherboard and RAM are good, so the laptop is essentially functioning; and your 2 hard drives have failed and need to be replaced and Data Recovery techniques need to be applied. Pictures of your model I found on ebay showed an HDMI video out port as Mike suggested, but it's obvious you have some sort of a sub-model variation that doesn't have it.
If however, your test drive is either not seen by the Vaio BIOS or will not install Vista from your Recovery Discs, then the Motherboard and or RAM is hosed. Did your wife recently drop the laptop or spill Pepsi on it (a la the movie "China Syndrom")??
If this is the case, it could be part of the reason that BOTH hard drives failed at the same time. At this point, I would suspect physical damage to the laptop. And your hard drives are generally not going to be recoverable by you using ANY software tools, Linux or otherwise.
Mike's idea of testing them out with a SATA/IDE usb drive caddy on an older XP machine, a desktop would be preferable is a great idea and one I use often. That takes the version of Windows you are using to test off the table.
If neither of those hard drives work in Mike's test scenario they are most likely gone and my comment above about professional data recovery still applies.
I have worked for 3 hard drive manufacturing companies over the years, and I know a thing or two about data recovery. If the drives are getting good power (you should test the DC power with a Multimeter on the power source to make sure), and the drives aren't spinning; you are pretty much out of luck with what you can do. They need to be sent out to a professional drive recovery service where they can actual disassemble the drives in a clean-room and do forensic data recovery. There are only 2 companies in the U.S. that do this reliably and I have used both with great success. If you reach this point, and you have to send them out they are:
#1) Geek Squad (Best Buy) located in Memphis, TN
#2) OnTrack located in Minneapolis, MN
Both these companies charge from $250-$20,000 and up depending on how close to 100% of your wife's data you need to get back, and how soon you need it done.
At this point, you'll need to have a serious sit-down conversation with your wife and ascertain the value of the data on those 2 hard drives. If it's pictures, and music, are those replaceable? And at what cost? Certainly, if they are family heirloom photos which no longer exist and were scanned into the computer--those are generally priceless. Also, if you had Tax information from programs like TurboTax or Quicken--vital; and which programs are on which 2 drives? Did you use the 2nd hard drive for storing all the data like Pictures, Music, Tax Folders; or was it spread over both drives? If that's the case or you just don't know or she doesn't know, you'll have to double that cost estimate I provided above since you'll need to perform data recovery now on 2 drives.
Hope this doesn't shock you too much, but I do this all the time and that's an honest picture of what's involved. Many people can replace or piece that vital information back or just can't afford the cost; but that's a decision only you can make.
I'm guessing you didn't have external data backups either, right? Or backup on the Internet Cloud?
Get back to us with your information and we can guide you further.
Best of luck.
BIGBEARJEDI