Though it's probably overkill and superstition, I'd assign something to Line first, even if it's just Line = "" or Line = " ",
then I'd put a Write, just under the Read, to write out Line and test it with data content. Finally, just hit the enter key as before. I do understand that it hangs after the Read with just Enter, you may not get to the Write in that case.
I'm suggesting those steps because it more clearly brackets the issue. And it would be interesting to see if hitting the space bar and Enter works too. I mean a <space> in this context is just as fine as a letter or other data.
Also, I'm suspicious of that 80a1 format. Can you make it more generic - What does Read(*,'(a)') line do in its place (with data and with just an enter? or try 1a1 and test with one character.
Are you using a Mac or PC Platform?
I would have tired some of my suggestions first, but I can't just copy the code you provided and run it here. It doesn't like the
Read(*,1) line
1 format(80a1)
construction. So I'd need your I/O statement in there too - something so I can duplicate the same success/error result.