Question: I just moved into a new home that has a backyard composter (about 80 gallons). The composter has been sitting unused for an unknown amount of time (at least 3 months).

How can I assess the health and status of the compost pile, and then what should I do to revive it?

Answer: 
Dig around in the compost to check the conditions and if the contents are ready to be used. Good compost looks like regular soil and has a light earthy smell. It should not smell badly or be very wet. Unfinished compost has lots of recognizable pieces still in it. 

Most likely the majority of materials left in the composter are transformed into compost by now and can be applied directly to your garden. Since you don't know what the original materials were I personally would not use it in a vegetable garden, only in other parts of your garden, but I am rather picky about what I add to plants my family and I eat. I tend to compost only organic material.

You did not say what kind of composter you have; a sealed bin or something placed directly on the ground with open bottom. If it's a sealed bin you can choose between regular composting and [vermicomposting](https://sustainability.stackexchange.com/tags/vermicomposting/info). If it's directly on the ground, worms will find their way into your heap by themselves.

There is no need to revive anything. If the bin is not smelling you can add new materials straight away, but personally I would empty it first and then start from scratch so I know exactly what the resulting compost is made of. If you want to do vermicomposting in a closed bin make sure you have some soil and worms as starter material. For regular (hot) composting soil as starter is not a necessity, but is [recommended because decomposition will start quicker](https://sustainability.stackexchange.com/q/15/99).
I agree it is a good idea not to use the compost left in the bin on anything edible or valuable. Just scrape it out and start again. They might have been composting meat, in which case it will be full of maggots and harmful bacteria. The idea is, if it smells spread it out in an out of the way place and let the air and the worms get to it.