Help me please [activate CS6 on a new computer]

You likely can't since the old PC won't start. You can't deactivate CS6 from the old device.

Time to replace with supported apps built for new computers.

MODERN OPTIONS:
==============
FREE Acrobat Reader
https://www.adobe.com/acrobat/pdf-reader.html

FREE Online PDF Editor
https://www.adobe.com/acrobat/online/pdf-editor.html\

Paid Acrobat (Standard, Pro or Studio)
https://www.adobe.com/acrobat/pricing/compare-versions.html

Photoshop Elements (3 year license).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Annual Photography plan. 
https://www.adobe.com/creativecloud/photography.html

Creative Cloud Bundles & Single Apps for mobile, web & desktops
https://www.adobe.com/creativecloud/plans.html

Hope that helps. 

and deactivating your laptop is very risky.  you're more likely to end up with no activations instead of two.

If you can't deactivate from the PC, you will have to deactivate from the laptop in order to free an activation for another computer.

https://community.adobe.com/t5/download-install-discussions/signing-into-and-activating-legacy-adobe-applications/td-p/14372541?linkId=100000353607574