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
When you have both devices plugged into, go your start menu, right click on Computer and select Manage. This will bring up your Disk Management function than look to see if there is a conflict with drive letters & one not being assigned.