How to decide whether a real life problem can be dealt with by computers?
The way we decide is we try to solve it and see if we are successful; or we look to see whether someone else has solved it (e.g., in the research literature).

Usually the question doesn't really make sense, as it is not well-defined what it means to "solve" or "deal with" a problem.  It's not like in mathematics, where it is a crisp black-and-white.  Instead, one may need to measure how well computer systems can address the problem, in what contexts they do or don't suffice, what their strengths and limitations may be, and so on.

Normally, the way we assess all of this is through experiments, not mathematics: we try techniques and evaluate how well they work empirically, and see what we can learn from that.