The symptoms sound as though the device is connecting but it has lost just the ability to get a drive letter assigned [one of my external drives has this problem but otherwise works well].
To assign a drive letter, use Computer management:-
0 Connect the errant drive
1 Type manage in the Start menu search box, right-click on the Computer management shortcut that is offered & select
Run as Admin. You will then need to enter an Admin account name & password.
2 In the window that appears after a few seconds pause, select Disk management.
3 Look at the list of disks-partitions to positively identify the drive concerned. It may be the only one that has no drive letter assigned but may not be [you might, for example, have a recovery partition or some other vital partition that does not need
a drive letter for its operation]. The list & the illustrations underneath show you many properties of the drives so you should be able to identify it.
4 Only when you have positively identified the correct drive, right-click on it & select
Change drive letter & paths... and then click on Add...
5 Next to the entry Assign the following drive letter, the system will offer you the next unused drive letter. You can choose any drive letter from the dropdown list. Choose one you do not use for anything else as this solution should hold for
all future use and you don't want to have a clash with any other devices.
6 Press OK, OK then close the Computer management window. The system will warn you that this will disrupt any current processes that refer to that drive [but there will be none that matter as the drive had nothing assigned before].
Please note that this solution should hold permanently [including after rebooting] but I find that some drives can lose the drive letter assignment after operations like formatting or after use in certain other machines. My problem drive needs to be re-assigned
every time I connect it but all the others just needed to be set up once.