I have used turbo tax for the past several years but filed on a different computer this year. Can I access the previous two years returns through this site?

If you used the CD/Desktop version that you physically installed on your computer, the tax file created is in the documents/turbotax directory on that computer, and has a filename extension of .tax20xx where "xx" is the two digits of the year. The only place that tax file exists, is on the computer where you created it, unless you backed it up and/or copied that .tax20xx file elsewhere.