If you've reinstalled Windows, this won't work, but here's something that might get you a date close to the purchase date:
http://www.redmondpie.com/how-to-find-out-when-did-you-last-installed-windows/
Knowing when the first date a particular Windows install occurred is not exactly what the OP asked. A clean install of Windows, for example, would "reset" the clock.
This really sounds like the OP has a warranty related question.
Most companies would be able to give you a rough date of manufacturer and warrenty period if you by supply the serial number. Can you not check via bank statements?
Just check your bill or your bank account for the day of purchase.
If it's a major system builder like Dell, HP, Acer, Gateway, etc... You can easily find the information if you enter your serial number on their website.