Is it permissible to use programs from the Internet for a non-commercial school assignment, knowing that one cannot afford to buy them and there is no other source to obtain them, and that seeking permission from the owner is not possible?

If the developers of the programs do not prevent their utilization, then there is no harm in that. However, if they explicitly state a prohibition, it is not permissible to infringe upon their rights except with permission, because these are owned rights for which money and effort have been expended, and copying them nullifies these rights. The resolution of the Islamic Fiqh Academy states that copyrights, inventions, and innovations are legally protected and it is not permissible to infringe upon them.

Some scholars permit personal use only, although the prevalent fatwa is a complete prohibition.