Right, a quick scan over the datasheets for the convertors you mentioned.
I realise you said these were on professional boards, but I'm intersted in what these boards have on them, as well as their real application.
Both the ADC and DAC you mentioned are unipolar..that is, will only accept a positive voltage. So at the very least the input from your laptop should be AC coupled with a cap, and a DC offset so 1v p-p becomes 0-2V centred around 1v (or half your power supply). As well as that I would have thought the board includes a opamp buffer, and possibly a low-pass/antialiasing filter.
Now thats the 'analogue front end'. Assuming the ADC does its job...what are you using to control this? Both ADC and DAC are SPI devices...so you could tie their data lines and clock lines together, but you would still need a 'CS' line to control when samples are transfered.
The DAC however, requires a similar interface, but with a 'sync' input. Looking at it, the data format is 16 bits....first two bits are 'don't care', then next two are power down control, then your 12 bits of audio data. The 'sync' input determines when the DAC recieves data. Similar to the CS line in SPI.
As far as the boards you have go, I'm sure the analogue can cope with audio, but bare in mind....in the datasheet, audio wasn't mentioned in the app notes. That doesn't mean they can't be used for audio, they're fast enough after all, but the boards you have might not contain the circuitry for audio (AC coupling, impedence buffer etc...).
So.....I would guess that if you've just connected these two devies together, running them off the same clock for Sclk, and tying the data lines together, the data formats are wrong, BUT similar, which means it probably is getting some form of audio data through, but constantly out of sync.
Now IF you have something taking the data from the ADC, formatting it then sending it to the DAC....then I would say its the analogue side. Perhaps some info on this boards and the saetup you have might be useful.
Regards,
Blueteeth.
Ps. Made a lot of assuptions there, sorry if I'm being patronising, just trying to help.