Is it possible that they are in fact PDF files that were for some reason relabeled .tax2013, etc. Try changing the file type to PDF and see if it opens as a PDF file. If not then change back to .tax2013. You could also try copying they file and changing the copy type to PDF. See what happens.

did you do a search on *.2013 on your harddrive??? maybe there are two sets of files for some strange reason. 

did you try opening them with Adobe just to test whether adobe seems them as *.PDF files? 

Did you reinstall the programs?  After you get the program installed the first thing to do before you open your tax return is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW TAX RETURN)

BUT it is too late to update 2016 and prior or download any state programs.  

OR you could try the TaxPrinter service to convert a .tax file to pdf at

http://www.taxprinter.com

They might be expensive and it is probably not safe to email tax returns back and forth.  They are not related to Turbo Tax.

Thanks for all the suggestions. I have solved the problem. 

All my TT files for 2013-14 were saved on my back up drives, carbonite, and cdrom I create for additional security. ALL showed my TT files with the correct .tax2013 extension but with adobe acrobat as the file type. How this happened is mystery to me. Other years are just fine.

So took one of the 2013 TT files, right clicked to get "properties", and could see that the file was "linked" or associated with Adobe Acrobat. I clicked on "change" and associated it with my TT 2013 application.  

Now it loads in to the 2013 TT app.  Tried the same fix for my 2014 TT files. Now they load in that year's TT app. 

FYI before fixing it, I did try to change the .tax2013 file extension to .pdf. It would not load in adobe or TT software.  I do save all tax returns to pdf files as well. FYI I could find any way to load pdf TT files into the app.  TT says this can be done, but it did not work for me.  

No you can't open pdf files in the program.  In certain cases you might be able to Transfer in the prior year pdf but very limited info will transfer if you can transfer it at all.