How can I repent and seek God's help to repay a debt I took from a financial trust in my house without its owners' knowledge, and what is the way for a repentance to be accepted and a prayer to be answered?

It is not permissible to take anything from a deposit if one is unable to repay it. This is a sin, and it is even more so if the owner of the deposit does not consent. The taken money becomes permissible by returning its equivalent. Eating from unlawful earnings may prevent the supplication from being answered, but this does not mean that answering is impossible. Rather, Allah's mercy and grace may override this impediment. Therefore, one must not despair of Allah's mercy, but rather increase in supplication and seeking forgiveness.