It was completely clogged and disgusting and the propeller was off. Does that mean it is broken?
Yes, it needs to be replaced.
Even if it was not broken and just clogged I would replace it with a new one as the blades can get dull over time.
I have found from experiance that if you had to clean the screen off once it most likely will end up clogging again, so I just replace them the first time around.