I can't activate my illustrator cs6 licence on a new device due it being install on broken computer

You might also want to look at the options offered here: 

CS6 Is no longer supported by Adobe. You can try and contact Adobe directly through the customer support page for help with activation. There are reports, however, that Adobe has not been able to help when the activation limit (2 computers) has been reached.

On the other hand, if you are now using a new computer with an up to date operating system then that system most likely does not support CS6 anyway. Subscribing to Creative Cloud may be your only option.