Take a look at the original sentence again:
Fred blew and blew on the globs of liquid white-out, but they refused to
dry when the professor called time, Fred
closed the cover of his exam book and hoped the pages wouldn't cement together.
You wanted to fix it this way:
Fred blew and blew on the globs of liquid white-out, but they refused to
dry, when the professor called time, Fred
closed the cover of his exam book and hoped the pages wouldn't cement together.
To add a comma between dry and when would cause an equally bad problem, a comma splice. A comma splice occurs when you have two complete sentences joined with just a comma. They refused to dry is the first sentence. When the professor called time, Fred closed the cover ... starts the second sentence. The spot between dry and when needs a stronger break than a mere comma.
You might want to consult the rules for fixing comma splices and fused sentences.
Go back to the sentence to try again.