Take another look at the original sentence:
You wanted to fix it this way:
To add a comma between began and when would cause an equally bad problem, a comma splice. A comma splice occurs when you have two complete sentences joined with a comma alone. Aisha hoped to get to her car ... begins the first complete sentence. When she found the doors locked and saw her keys lying on the front seat, she knew ... starts the second complete sentence. The spot between began and when needs a stronger break than a wimpy comma.
You might want to consult the rules for fixing comma splices and fused sentences.