Can I download the tax software for 2013 from Turbotax?

Sorry no.  They only go back 3 years.  Even if you find 2013 online somewhere you wouldn't be able to update it or download the state programs.

Here are some blank forms & instructions for 2013

1040 http://www.irs.gov/pub/irs-prior/f1040--2013.pdf   

Instructions http://www.irs.gov/pub/irs-prior/i1040--2013.pdf

1040A http://www.irs.gov/pub/irs-prior/f1040a--2013.pdf

Instructions http://www.irs.gov/pub/irs-prior/i1040a--2013.pdf

1040EZ    https://www.irs.gov/pub/irs-prior/f1040ez--2013.pdf

Instructions http://www.irs.gov/pub/irs-prior/i1040ez--2013.pdf

2013 Tax Tables  http://www.irs.gov/pub/irs-prior/i1040tt--2013.pdf

Publication 17 Tax Guide for 2013 http://www.irs.gov/pub/irs-prior/p17--2013.pdf

2013 Form 2210 http://www.irs.gov/pub/irs-prior/f2210--2013.pdf       Instructions http://www.irs.gov/pub/irs-prior/i2210--2013.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.