Unfortunately, no. The 2014 tax file would have been stored on the computer that it was prepared on, so the only way to gain access to it would be on that computer.
Don't you backup your files? If not, you have learned a very painful lesson. I am surprised you have not had a similar problem with other files. Maybe you were just too lucky.
With your newer computer you have a few physical options for backup; FYI: Do not use your "C" drive ever for backups; 1) another disk in your computer, 2) a USB drive, 3) a CD drive (but then you need a physical storage area that is clean; then worry about something happening to that CD if you don't password your files, 4) a NAS drive for which you have backups (FYI: I have a Synology NAS drive that does its own backups and allows me access via the net through my router and network switch).
You might also want to consider some stand-alone backup packages (MSFT has it on the menu bar that comes with Windows if you use that; MACs have similar backup capability (Time Machine). I use GoodSync from Siber as it also shows me which files have changed BEFORE I do a sync.
Good luck, anyway.