I will try and get it right this time, my spouse and I where married in Dallas,Paulding County, ga. I 1996, she left the marriage in 2004. Since then I have been trying to contact her about giving me a divorce.I have advertised in the newspaper, with thephone number I had 2 years ago.Since then I have not received a note telephone
Call or anything that would give me a clue as to where she might be served.My question is can I file abandonment charges against her,so thatI might get a divorce without her signiture? I am ready to move on with my life.
Thank you,

The Court can order that you publish a notice. If she does not respond you proceed with the divorce without her consent BUT you must publish by Court order in a Court-recognized publication using Court-ordered terms.

Ever see the word "Court" so many times in one sentence?

... can I file abandonment charges against her,so thatI might get a divorce without her signiture? ...

A divorce, like any other lawsuit, can happen without the other party's agreement (signature). You get her served with process (notice of the lawsuit, perhaps, as JudyKayTee suggested, by publication). Once she is served, she has so many days to respond. If she doesn't, she can be defaulted and a divorce decree entered whether she agrees.

Abandonment used to be one of the grounds, available in some places, for divorce. It is not necessary any more because "no-fault" divorce (i.e.: a divorce in which one party doesn't have to allege that the other party is somehow at fault) is available everywhere in the U.S.