A look inside will reveal a cylindrical-shaped capacitor that has swollen and spewed some of its internals. A wet spot is a clue. A puddle of dried, brown or tan powder will be left behind if leaked liquid dries out.
This kind of part usually fails as a short circuit when they go "POP" like that. The next question is what collateral damage it did. A short circuit in a capacitor can overload other components and damage them. In particular, the components in the power-supply regulator are vulnerable.
If you can hook it up to a 12-Volt DC power supply, you could find that the radio is okay, and only the built-in power supply is bad.
Maybe. But a good look inside for a swollen or ruptured part is a better place to start.
Safer than just hooking it up to a DC supply and crossing your fingers.
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