in reply to The or thing.

It seems to me that you need to put parentheses around the entire 'if' statement (both tests):

if ((-e "$file.data") || (-e "$otherfile.data"))

When I run your test this way, I get the Hooray message. When I omit the enclosing parentheses, I can't even get the thing to run - so I'm wondering what it was that you were able to get working.