If your Google API key is not working, then the plugin should fall back to the built-in list, and that does include "Alfa Slab One" (standard weight and style only). Is that working for you?
It looks like two separate issues here: some API keys not working, and the fallback list not working when Google cannot be contacted. So just to be sure, are you having both of these issues? If you don't put a Google API key in at all, do you not find "Alfa Slab One" available in the drop-down lists of fonts in the Woothemes theme?
If you put the following into a post or page, do you see the font or not:
[typography font="Alfa Slab One" size="24" size_format="px"]Test font[/typography]
You can test your Google API key by putting it into a URL, like this:
You will either get an error, or a big list of font data.