The hub pawls sound like the problem as you stated.
Inside the rear hub there are pieces that engage the wheel when the chain is pulling the cassette forward. But they disengage when you're not pedaling, so the wheel can still spin without the chain moving.
The question is why?
Are they just gunked up with old grease? Is the hub broken and needs to be replaced or repaired?
Even if the hub had the be replaced completely this shouldn't be a terrible expensive repair. And the shop should be able to give you a reasonable estimate right away. But of course they could take it apart and realize that not only was the hub broken but so was something else, which would add to the cost.
Still....this should not be terribly expensive.