If your old computer no longer works then you would need to contact Scott Vibert (scott@greydogsoftware.com) to have your license deactivated from that machine so that it is available for use on your new system.
You would need to tell him your license key. This is the code that you received by e-mail that begins "VT-".
If you do not have this, you would need to tell him your name, e-mail address and, preferably, the last four digits of the card used to purchase the license so that he can look it up.
I don't know what you mean by "computer ID" or why you are looking for this, but to clarify, you cannot deactivate the license from your end if you do not have access to the broken computer.
NB From your wording, it sounds like you have mistakenly downloaded the QLM (*) version of the game; you are unlikely to be a QLM license holder as that is a relatively new system and you said you are not a new customer, so you would need the Elicense version of the game. You can download it from the TEW2016 page, using the Elicense Download button on the right-hand side.
(*) QLM is the license system we now use. Elicense is the one we used to use. They are not interchangeable, so you can only use the QLM version of the game if you have that type of license.