Can you still use a sewing machine if the feed dogs are not working

You could no longer do standard seaming, but you could do free motion embroidery. 
If you want to fix this there are a few common ways that they get broken and fixed from home:
thread could be jammed, just remove the needle plate and clean
hasn't been lubricated in a while, either take it in and have it done or do it yourself with a drop of sewing machine oil
or because they're dropped, in this case just look for a switch.
if it's not any of these, you may want to take it in and have it looked at :-)

Would it be an oboe?

What do you mean by this?