No ... Turbotax only supports tax years 2015 thru 2018. If you need to complete a return that old you need to get the forms from the fed & state websites and complete them manually OR seek local professional assistance.
If you want to get the blank forms to fill out by hand,
Here are some blank forms & instructions for 2014 to get you started
2014 Tax Tables https://www.irs.gov/pub/irs-prior/i1040tt--2014.pdf
Publication 17 Tax Guide for 2014 https://www.irs.gov/pub/irs-prior/p17--2014.pdf
Don’t forget your state. And you will have to print and mail your returns. So be sure to attach copies of your W2s and any 1099s that have withholding on them. You have to mail federal and state in separate envelopes because they go to different places. Get a tracking number from the post office when you mail them for proof of filing.
Sorry those were for 2014. Here are 2004
Here are some blank forms & instructions for 2004