I don't think that the adapter is the problem if you see the drive in DM. But what do you mean that the drive has no letter? The operating system assigns a letter to every usable physical drive and/or partition in order to enable user's access to drive by means of a file manager/explorer. Usually, only system partitions, recovery partitions or other kind of partitions that shouldn't be accessible to the user are not assigned a letter. So, if your drive has not a letter assigned to it, then you can not access it. As you said in your initial post, the old drive has an operating system installed on it. This means that, probably, your drive has more than one partition. In DM you should see your drive as it is divided in a few parts. The largest part (partition) should be the one you are looking for and it probably had been assigned the letter C in your previous computer. You should right-click on this partition and from the pop-up menu that will show choose Change letter and then pick an unused letter from the list and click OK. After doing this, the drive will probably appear in Windows Explorer.
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