I could be wrong but I think you need to use the original computer you initially used to file additional taxes. I purchased the same program and filed my taxes and my girlfriends from my computer. You can file 5 returns on the same computer. Hope that helps....
The TurboTax user license allows one user to install copies of TurboTax on up to five computers that the user owns. You can also prepare multiple returns, including returns for other people. But the license does not allow, and has never allowed, one copy to be shared among different people. This year, that license is being enforced by requiring users to log into their TurboTax online account when they install the program for the first time. This locks one particular copy of the program and one license code to one user account. The only way you could install the program on a computer that you do not own, would be to give the other person your online username and password. And even though that workaround might allow the installation, it’s still a violation of the license.