Take another look at the original sentence:
You wanted to fix it this way:
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 prepositional 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.