"There is no hope!"
Translation:Det finns inget hopp!
ett hopp, inget hopp; compare to: en penna, ingen penna - it's inget because of agreement with an ett word [Disclaimer: I'm just a learner of Swedish, not even intermediate.]
See also http://learningswedish.se/courses/1/pages/pronouns#2.5
There, click on show rule to see about ingen, inget, inte and much more.
What's the reason for "förhoppning" not being accepted? Isn't it basically the same? "Inget hopp" - "ingen förhoppning".
A förhoppning is a little different, it's where hope meets expectation - and it's inherently positive. It's not something you'll ever find in an exclamation.