How do I go about resolving this? Proof of employment for the year 2000 stating I lived in Texas and New Mexico? Would my Federal tax return for that year work as proof?

“Louisiana is saying I owe them taxes for 2000 - I didn't even live there in 2000!” How do I go about resolving this?”----->Needless to say, you need to contact Dept. of revenue of LA (LA state taxing authority) for detailed information.
Please visit the LA Website here: https://esweb.revenue.louisiana.gov/...idual&type=tax
Revenue Offices : About Us : Louisiana Department of Revenue
“ Proof of employment for the year 2000 stating I lived in Texas and New Mexico? Would my Federal tax return for that year work as proof?”---->I guess so; a copy of your federal or state returns for 2000(a copy of New Mexico state return as there is no state income tax in Texas; Texas does not have state income taxes because the state government funds operations by utilizing property taxes instead) or a copy of property taxes that you paid to Texas at that time.