Reverse biased capacitor on IC input pin
Your description doesn't agree with that in the datasheet. Pin 7 is the output of the internal amplifier, and pin 8 is its input, designed to accept a low-level AC input (57 mV for a 0-dB indication).

It sounds like you're trying to drive this circuit with a signal that includes a considerable DC bias, which explains why all of the LEDs light up right away when you remove (short out) the capacitor.

However, if that's the case, I can't explain why reversing the capacitor doesn't work, unless the actual polarity of the capacitor is backwards from what you think it is. Have you tried a non-polarized capacitor (e.g., ceramic)?