Additionally, beyond the above posts that would indicate that most railroad routes leading into New Orleans are out for the foreseeable future, add to that the following:

While so far only light damage has been reported to the station that was before the flooding started. I have read reports that the station is at least surrounded by water, if not actually flooded. I have seen pictures of the yard leads that suggest that all approach tracks are underwater at present.

While preliminary, the Mayor of NOL has indicated that full power may not be restored to the city for two months. Residents have been told that their evacuation will last at least one month.

Amtrak has closed its crew base in NOL, and all workers are effectively furloughed. They can if they have seniority, bid on other jobs within the Amtrak system.

So I would bet on a minimum of two months, and more likely three to four months before any trains start running to NOL. It is quite possible that Reindeer is correct that it may be six months before full normal service is restored.