Well it's better to do it
I don't know why the sound was working through the headphone jack and then suddenly stopped, and it could well be a hardware fault, eg faulty jack or faulty headphones. But my consideration is that this system needs the correct system drivers for this model.
Faulty headphones can be checked of course, try them in a different computer and try different headphones in this computer, but a faulty jack is much more difficult to test, especially on a laptop. Unless something is clearly bent out of shape, any fault is going to be internal.
Other than that, what changed on this system when the headphones last worked? Any updates or malware or anything else?
But overall I believe that this system needs proper motherboard/chipset, sound card, video card and ethernet drivers. Not from Microsoft, although Windows 7 does seem better at finding drivers we still recommend going direct to the make/manufacturer.
I found this link for your model Sony Vaio; http://www.sony.co.uk/support/en/product/VGN-FZ21M/tips-and-solutions but I see this model was for Vista and although Win 7 is mentioned, a quick glance didn't find me those drivers for Win 7.
Note the link is the UK branch. If you are in the US the search term was [url sony vaio vgn-fz21m drivers [/url]