Is it permissible to work if the primary reason for it was originally an unlawful act?

There is no harm in your work if it is permissible. The reason you mentioned (downloading a pirated program) does not affect the validity of the work, as it is not among the conditions or pillars of work. Work is only considered in terms of its contract, field, and outcome. God's grace and your expertise are the real reasons behind your employment, not your use of a pirated program. Therefore, you should ignore these obsessions so that they do not turn into whispers that lead to doubt.