Hi Simon,
Welcome to the forum! RESET must be high or the device will be held in reset. START must also be high to read and write register values. The CLK must be tied low for use of the internal oscillator, or you must provide a clock. I would also suggest that you connect AVDD and AVSS to the +3.3V and GND at this time as well.
One other consideration and that is CS must be low throughout the entire communication transaction (not just each byte portion of a multi-byte communication transaction).
You might also take a look at the ADS1220, which is very similar to the function of the ADS1247 but has simpler operation.
Best regards,
Bob B