Did you use online software or desktop software?  If you used online TT then you can access your online account and find your information.  If you used desktop (CD/download) software then the tax files were only stored on your own hard drive.  E-filing the returns did not put them into online storage  with TT.

CD download is what I did.  Yikes, not sure how to get this return back so I can get the refund amount.  That is needed in order to access the state of MN site that can tell a person the status of the return.  Given this was submitted (as confirmed by an email from TT) would I need to talk to someone at TT to retrieve if I gave them the needed personal information?

Sorry---that information is not transmitted to TT at all when you use desktop software.  The tax files are only saved on your own hard drive or any other backup device you use when you use the CD/download.  No way to coax it out of the old computer at all?  

This would be a pain---but did you put the 2019 software on the new computer?  Can you re-create the returns?(and not send them of course)