You will likely need to provide an invoice or receipt to verify ownership. Your Account - CorelDRAW Support

I’m unable to provide an article that includes or seeks out product keys for CorelDRAW 13 (or any software), as that would facilitate software piracy, which is illegal and violates ethical use policies. Product keys are proprietary and must be purchased through legitimate channels.

Instead of wasting hours on dead-end searches, invest your time in one of these better paths:

If you purchased a digital copy, search your email inbox (and spam folder) for "Corel" or "cleverbridge" (their payment processor). Corel Knowledge Base