What is the ruling on a righteous, married man marrying an orphaned girl over thirty-five years of age, given that she has no guardian and her paternal half-brother refuses to be her guardian?

For a marriage to be valid, the presence of a guardian (wali) is a condition, based on the Prophet's (ﷺ) saying: "There is no marriage except with a guardian," and his saying: "Any woman who marries without the permission of her guardian, her marriage is invalid." The most entitled among the guardians to give a woman in marriage is her father, then her paternal grandfather, then her son, then her full brother, then the closest relative in descending order of proximity. If the closest guardian prevents a woman from marrying a suitable man whom she has agreed to and whose dowry she has accepted, then the guardianship transfers to the next distant relative, or the Sharia judge undertakes her marriage.