For some reason the template path hints are not displayed.
I went to the admin panel and turned them off and on again, then cleared the cache. But they are still not displaying.
How can I debug/solve it?
Try to check if your configuration backend for System > Configuration > Advanced > Developer Client Restrictions is empty or set to your correct IP address (the last case is the best pratice).
Or to follow the idea of @fabian-blechschmidt, check if you didn't have overwritten one of the methods in your Block:
It may help
use an extension instead
This will save your time going into the backend each time you want to enable template path hints.