I have a new computer and wondered if filing this years tax return there is access to prior filings?

If you are using TTax On-Line simply log into the same account you used in previous years.
If your are using the Desktop version (installed on your computer from CD or download) then YOU need to copy the .tax files yourself from the old computer to your new computer.

By default TTax data .tax files are stored in the My Documents\TurboTax directory with a .taxyyyy file (yyyy = the specific year).