The State Archives would not have the marriage record. Only if they were married in Orleans Parish. West Baton Rouge Clerk of court would have the record though. On the few marriage records I have from West Baton Rouge Parish, the parents names are given. But, I do not have any from that parish that date as back as 1835. Call the clerk of court, they would possibly mail it to you. Sometimes for the cost of the copy, and the cost of the stamp.
State Archives would have death records for 50 cents per copy, if you pick up. Or $5.00 to have them mailed.