Is it obligatory to pay a diagnostic fee for a refrigerator, considering that the technician did not inform [the owner] beforehand of the existence of a diagnostic fee, and refused to take the refrigerator as a gift, then dropped the fee after an argument, then left the country?

If inspecting a refrigerator and identifying a defect usually warrants a fee, then a fair market wage (ujrat al-mithl) must be paid to the technician. The fair market wage is determined by experts in this field. If it is impossible to deliver it to him, then it should be given as charity on his behalf.