Designed an electronic circuit using APR33A3. Not working
The question as it stands is impossible to answer because it lacks your schematic, but since you are looking for suggestions I have a few.

Verify voltages

As Eugene pointed out in a comment, you must look at the voltages on each relevant node while operating your circuit. This would be everything with a VDD in front of it. Preferably with an oscilloscope, but a multimeter will do. If it measures lower than expected or if the value fluctuates "too much" you have a problem. Add more bypass capacitors and see if it works.

Speaker

The datasheet does not tell you that you can connect an 8 ohm speaker directly. It's a lousy piece-of-crap excuse for a datasheet, but it vaguely hints that the maximum current out of VOUT is "typically" 185 mA. I assume it's putting out +/- 5 volts there, and 5 volts through 8 ohms means 625 mA. Ideally this should still work but give you a lower volume than expected, but worst-case it tried to drive 625 mA, couldn't do that, and fried something in the process. Somewhat unlikely, and the mic LED should still work, but hard to say.

Supply

There's a couple of voltage rails involved here, each with a separate ground pin. If you're just breadboarding this and the grounds are not well planned, this could cause all sorts of problems, difficult to debug without an oscilloscope. The problem is that wires and breadboards look like inductors and resistors to the signal, and when current flows through them it causes voltage drops and ringing. Dozens or hundreds of books have been written about this, but what you could try is to connect each ground pin of the chip directly to one point, called a star ground. In addition to this, it's important that the decoupling capacitors are very close to the chip.