OK, for RS-232 a very convenient rule of thumb is that you will be close if you figure 10 bits per character (start-data-stop). So for 2 bytes/value (you need ID/synch) times 8 channels and 2000 reads/sec you need to transfer (2*8*2000) 32000 bytes = 320.000 bits per second. To the best of my knowledge, the PC is not capable of that rate on the RS-232. You need to decrease the read rate in order to use PC RS-232. Or you can install a turbo board, such as the TC-200 which will allow you to go to 460k, but that will still be a potential troublespot.
If you MUST have 2000 reads of 8 channels, look into the Cypress Semiconductor EZ-USB '51 based chips - I have not used them - so just a suggestion - maybe someone will chime in on that. With careful coding and interrupt driven serial transmission and parrallel read of the ADC's any decent 24Mhz doublespeed '51 with a double DPTR can handle your task.
Have fun,
Erik