I have the same problem! One of my letters is photocopied, the professor is no longer at my school (therefore I cannot get it on letterhead) and its not even signed because she sent it to me in an email (therefore it looks like I could have written it...). I really don't know how they can expect us to give them an original, most teachers will give you one and then drop off the face of the planet (ok maybe not...)
I have been trying to get ahold of my professors for WEEKS now and the school is not even in session right now, so I feel like I'm screwed. Thinking about just putting an addendum behind the letter stating the reason for its unoriginality? Any opinions??