The information shown for the second HDD unit, "Disk 1", says it contains one tiny Partition of 200 MB (0.2 GB) as a "System Partition" with no letter name. It has been made deliberately difficult to access to prevent alteration, and that Partition with no name will NOT show up in My Computer. Likewise the tiny left-over block at the right end labeled "Unallocated Space" of 0.12 GB is not a "drive" and won't show up. But now look at the major middle block that contains 299.77 GB and is said to be a Healthy Primary Partition, but with no letter name assigned. The lack of a name means it also cannot be shown and used in My Computer, but that should be fix-able.
First important question about your screen shot: how did that mini-menu show up? - what did you click to get it? Ideally, you should be able to RIGHT-click on that middle 299.77 GB Partition to get such a mini-menu. BUT one of its choices available should be to Change Drive Letter... In your screen shot that choice is grayed out, which I can understand if the right-click was done on either of the other two blocks. If you can get the choice to Change the Drive Letter of the large middle Partition, just choose that and give it any letter not in use already. If that works, back out of Disk Management and reboot Windows to get it working.
By the way, you should realize that the Lower Right pane of Disk Management SCROLLS to show you all the disk devices. I note that the Upper Right pane shows a Disk called "D:" of 200.43 GB size that is not present in the lower hardware list. That makes me think there is more to be seen there.
For clarification: is there data on this HDD you need to preserve? Not clear from your post. If there is data in that large middle Partition with no name, that makes it a good idea NOT to Delete the Partition and start fresh. But giving it a letter name as I suggest will do no damage to its data.