I suggest that you take the external drive to a repairer and have them remove the drive and install it in a machine to see if the data can be accessed.
If the data can be accessed by a repairer, then the cost shouldn't be too bad, perhaps $100-$300 dependent upon the amount of data that needs to be recovered, and if the data can be simply recovered by installing the drive in a new enclosure.
If a repairer cannot access the data and the drive needs to be sent to a service that specializes in data recovery the cost could be quite high, and you would need to determine if the value of the data to be recovered would be worth the cost.
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