When you try to activate Parallels Desktop with your trial key, the following message is shown:
Parallels Desktop cannot connect to the Internet in order to complete your product activation
No activation ID is shown.
Trial license has expired.
You already requested a trial license for Parallels Desktop in the past. Trial license is provided only once and is given for 14 days. When 14 days expire, the trial period cannot be extended.
For more details about Parallels Desktop trial, please visit: https://kb.parallels.com/116845
The only way to continue using Parallels Desktop would be to purchase the full key.