Am I sinful for having used a program for six months with a fake activation key that a computer maintenance shop put on for me without my knowledge, and must I donate the value of the program on behalf of the owning company if reaching them is difficult?

What the shop owner did is impermissible because software piracy is an encroachment upon people's wealth without right. There is no sin upon you for using the program during this period due to your ignorance, but you are required to compensate the company. If you are able to deliver the right to its owners, then that is obligatory; otherwise, spend it on charitable causes.