How to check IC chip?
Not really - the way to check that an ADC is working is by testing it as an ADC. It is a complex device with potentially millions of transistors internally. Each one differs in design, and although someone with a full design knowledge of the internals might be able to infer something with basic probing, they would likely instead install it into a known working circuit configuration.

I would check my code, check to see if there is a self-test function documented anywhere in the datasheet and if I couldn't get it working at all consider swapping the IC out for a replacement. That said, if you don't know what may have killed the ADC the first time, this risks just throwing another one to its slaughter.

Brian Drummond's comment about an oscilloscope is a good one - with this you could look to see if the data lines were behaving consistently with timing diagrams in the datasheet. You could also use a logic analyser for the same thing, if you had one handy, or at a pinch program another microcontroller to act as a sort of logic analyser for this task. You are going to struggle to design any electronics without an oscilloscope though - you should certainly consider buying one.