The keys are stored in your Windows Registry...though if they are there, it should automatically find them and know not to have you in trial mode, and since you have rebuilt your machine that would likely have wiped them (if your rebuild included re-installing Windows).
If you want to find your serial key:
Hit the Windows Key and R, which will bring up a Run... window.
Then type "regedit" in that window and press enter.
Once there, navigate the tree to the location I indicated:HKEY_CurrentUser->Software->MountAndBladeKeys
On the right hand side you should see a list of things like serial_key.
(I'd then recommend recording it here on the website for easy future retrieval)
If there isn't anything there, you'll need to recover your key from whoever sold you M&B. If you got it through Taleworlds.com:
Did you buy it from the Taleworlds website?
Then try this link: https://secure.avangate.com/support/section.php?&avangate_template=1
Or this link: http://store3.esellerate.net/store/support/
(Found on Taleworlds.com, Sales FAQ http://www.taleworlds.com/salesfaq.aspx )