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Since both removable drives function OK by themselves, but not when connected together, it's probably a power issue.
You didn't mention what kind of removable drives these are and if you can connect them by a separate power cable.
Are these 2 TB HHDs both power and data connected by a USB cable?
Try connecting one to the computer, and booting up. Then when everything is running OK & that drive has spun up, connect the second one
If they have the option to connect to a power brick try that, or if you have a powered hub, try that.
That will rule in or out whether the 2 TB drives are supplied with insufficient current, or if it's a different problem