I got a ticket today for failure to yield at a traffic light which was not in service with no accidents and it was a main street that intersected a secondary street it was a street where you could only turn left or right. When I first started driving over 15 years ago it use to be the main street has the right of way. A co-worker came through the same light and the same officer gave her a warning. Should I fight this ticket and if so how?

It probably varies from state to state, but in many jurisdictions, a non-working traffic signal requires drivers to stop as if the intersection was a 4 (or more) way stop situation.
Only you can decide if you would have an explanation that would be satisfactory to a judge or magistrate.
I have gone to court in a few instances over many years and have never regretted doing so. Also depends on your driving record. They may consider the fact that the your direction of travel had the right of way prior to the installation of the signal, or they may scoff at it. Nobody can predict how the judge looks at it.

... it was a street where you could only turn left or right. ...

The other motorist was only permitted to turn left or right (no option to go through the intersection)? The fact remains, someone should have yielded. If it was a near miss because you figured you had the right-of-way, it seems to me that you will loose. If the light wasn't working, you should have stopped and only proceeded when it was safe to do so.