Your activation key can be found on your license page on pyxeledit.com. See Finding Your License
The key should have to following format:
----- BEGIN ACTIVATION KEY -----
Name
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
----- END ACTIVATION KEY -----
Make sure you copy all the text in the box on your license page (see image below).
If it looks like
ABCD-ABCD-ABCD-ABCD
then you need to use it on the following page to claim your license: http://pyxeledit.com/get/humble.php
or you can get there directly from your Humble download page by clicking the link under "Access your Pyxel Edit license page" that looks like ABCD-ABCD-ABCD-ABCD
Activation key on your license page
It's likely that the application isn't able to store the license to file because of permission issues.
Try deleting the data folder to let the program create it again. You can find it here:
Windows: C:\Users\[username]\AppData\Roaming\PyxelEdit\ELS or similar. You can enter %appdata% as the path in windows explorer to find the Roaming folder quickly.)
Mac: /Users/[username]/Library/Application Support/PyxelEdit/ELS or similar. Open Finder, then choose Go>Go to folder... from the menu to be able to enter the path.
If you have Pyxel Edit running, you can quickly find the ELS folder using the menu Help > Open storage folder, then going up one step to the parent folder (see image below).
Finding the ELS folder