Is it permissible to use pirated computer software to record and publish the Qur’an, and would the doer be rewarded for the listeners?

It is not permissible to use pirated software, even for the purpose of spreading good, because it infringes upon the rights of its owners. One who uses it, knowing it is pirated, will receive no reward, just as there is no reward for praying on usurped land or performing ablution with usurped water. Thus, "validity does not necessitate reward."