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You have two choices. One, is to pay the fee and fines outstanding just to get rid of the problem. The other way is to sue the California DMV for saying you have not paid when you actually have. If you are going to sue, you will need to provide some sort of proof that you have paid the fines and fees (for instance, an account statement showing that you paid the $50). You may not have evidence of the 2006 paid tickets, but if you can show that you paid the $50 and CA says you have not, then you can at least discredit what they are saying. I would suggest hiring a traffic attorney where your unpaid tickets are to help you out with the process.
As for the garnishment of wages, California could only garnish your wages after obtaining a court order against you saying that you owe the money.