Unfortunately, there is only one last ditch effort to free up that freewheel. The following link takes you to a very simplified diagram of how a freewheel works :
File Roue libre cliquet svg
What's happening in your instance is that the pawl, colored red, is not engaging the outer teeth, possibly due to corrosion, or age. What you can do is use a penetrating oil to get inside the mechanism to try to free it up. In the following link, you will see a freewheel that is most likely similar to yours:
Shimano Hyperglide Freewheel
You want to add oil to the edge of that inner ring that says "Shimano" (yours may not say that), while spinning the cranks to draw the oil in. Hopefully, after a while, and maybe a lot of oil, the pawls will free up and start catching.
Good luck!