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, as a result, when the professor called
time, Fred closed the cover of his exam book and hoped the pages wouldn't
cement together.
A comma splice occurs when you have two complete sentences joined with just a comma. They refused to dry is one sentence. When the professor called time, Fred closed the cover ... begins the next sentence. The addition of a transitional phrase like as a result does nothing to alter the fact that you have two sentences joined with a comma, thus creating a comma splice.
You might want to consult the rules for fixing comma splices and fused sentences.
Go back to the sentence to try again.