Is it permissible to marry an orphaned girl whose brothers - her guardians - have refused to marry her off without a valid شرعي (Sharia-compliant) reason?

We advise you to stop chatting with women online. If you wish to marry the girl, then propose to her guardian. If her guardian prevents her from marrying, then she may refer her case to the judge to marry her off or appoint someone to marry her off. Before marriage, one should perform Istikhara (prayer for guidance) and seek consultation.