Can anyone possibly tell me how to check if my AD7887 is working or not?
The AD7887 is 12 bit ADC. The Analog input can range from 2.5V to Vref. To verify that the AD7887 is working is basically it should have a correct digital result. The AD7887 output is straight binary, so a zero potential(GND) on the input would result in a 0x0000 while at Full-Scale output is 0x0FFF. The output has 4 leading zero followed by the 12 bit conversion result, thus the AD7887 requires 16 SCLK cycles for every data transfer. You may check the details on the datasheet for the digital interface for the timing diagram.
Do you have a current set up? You may share your scope shots so that we may also be able to see and verify if the results are correct. You may refer to the fig.11 of the AD7887 datasheet for the typical connection diagram.