Can I file for a divorce in my local newspaper in the state of Virginia for free?

What do you mean by that? To file a divorce in the local newspaper in virginia? Please clarify. All I know you can apply for legal assistance for the divorce.

You file for divorce in court. You do not file for divorce in a newspaper. Sometimes, if the other party cannot be found, you can serve them with notice through the paper, but that has to be approved by the court.

Have you spoken to legal aid yet?

Yes, using the "newspaper" is the most expensive way normallly, since the cost just to post as required can be 1000's of dollars.

But this is only a form of service, the actual divorce has to come though the court