Hi,
the simplest way to program the 24C512 is via the parallel port, if you have one, of your computer. The program can be done with Visual Basic to read the data file and serialise each byte into bits and then clock out each bit using a second line of the port. You will need to read the 24C512 datasheet very thoroughly to understand its addressing and timing requirements, it's quite a demanding project if you are not very familiar with VB or interfacing but should be fun.
It should be possible to make a system to play your sound file through a D2A without using a micro but I'd be tempted to use a parallel EEPROM, imagine a crystal which clocks a counter - the counter is attached to the address bus of the EEPROM and at switch-on starts from 0 and the output of the EEPROM is applied to the D2A, the counter increments to the next address and so on...
I think the important thing is that the crystal frequency should match the notional sampling rate of the original data.
Best of Luck