Yes I think the ~$ in front is a bad sign, it shows it is a temporary file.
Basically when you open a word document it creates a temporary file to work on (so the original does not get damaged or corrupted).
When you then SAVE the file you are working on it makes THAT the main word file (by removing the ~$), and deletes the other file.
So the fact you still have the ~$ in front means Word did not shut down properly, which is perhaps why it is not opening.
Go back to the original machine and see if you can find a copy of the file WITHOUT the ~$ in front as that will be the proper Word file.