Before we can help you with what the problem is, you need to find out where the problem is. If you are able to reprogram the microcontroller to perform tests that will make it a lot easier.
First, check that you have ground and Vcc properly connected on EVERY chip, and that you are receiving power to every chip from your power source. Use a continuity checker to check for a solid connection between the power pins and their appropriate bus.
Numerous troubleshootings, by myself and my classmates, have been resolved by "check your power".
Notably, I see on your schematic that Vs of the audio amplifier is connected to ground, not Vcc. Double check that.
If you did not make such an annoyingly frustrating error in your circuit wiring, here's some other things to consider:
Double check your address and data lines, and make sure they are going to the right places, if you can, use different wires for address, data, power, ground, and whatever else. There's nothing I hate more than seeing a spaghetti mess of wires all in just two colors.
Once that's done, isolate each individual piece and make sure it works. Make sure that the uC is reading the EEPROM properly by having it sample certain addresses and displaying them somehow, such as on an LCD screen or a serial terminal on a computer.
Have the uC send fixed values to the DAC, and measure the output to see if it makes sense.
If those things work, then you need to step through your program and debug that somehow.