Just replace the extension cord.

Probably not worth the hassle. Extension cords are cheap, and testing for internal breaks or shorts without a multimeter is frustrating and unreliable.

You can MacGyver a continuity tester with a battery, a light bulb, and some alligator clips. Clip the battery and bulb in series with the cord’s conductors, flex the cord along its length, and watch for the bulb to flicker — that’s a break. But it’s finicky, you need to know which wire is which, and the results are sketchy.

Shorts are even harder: you need to check resistance between hot and neutral, which basically requires a multimeter. Without one, you’re guessing.

Your time is worth more than the cost of a new cord.