What is the religious ruling on marrying a girl whose guardian agreed, then refused, then everyone agreed except the sick father who is unconscious, knowing that the marriage is contingent upon his consent?

The Shari'ah recommends accepting a competent suitor. If the guardian refuses to marry off the woman without a legitimate شرعي justification, she may refer her case to the Shari'ah judge to marry her. In the event of a long absence of the guardian, the girl can refer the matter to the judge, or the next closest guardian can marry her off. The previous guardian's refusal is not to be considered, because his guardianship has fallen away and transferred to the new guardian, who will consider the girl's best interest.