Here’s how it happened!
Analyzed The Problem
Took out my multimeter and started probing on the spring coils and the golden pins and checked for continuity. Realized that the working controller did show continuity whereas the one above didn’t.
Solution
Figured out that the problem is because of the rusting of the spring coil. A quick search showed that a vinegar-salt solution could help remove rust. Dipped the rusted spring coils into the magic mixture.
Assembled it.
Put various pieces back together. Installed the batteries. Took a deep breath. Pressed the Xbox button & IT WORKED!