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>>>"Use Disk Management. It will offer Logical for the fourth partition. Accept it. ."<<<
There are only 3 partitions in this PC:
1. C:\ where Windows 7 resides
2. the problematic partition (is hidden)
3. the other primary partition (is okay)
There was a 4th hidden partition that I did not create the "Recovery" partition which is now also been deleted.
Your first screenshot shows four partitions:

There is no Recovery partition showing in your Disk Mgmt screenshots as it would if you'd had one - the two non-OS primaries are empty. We would not have advised deleting it if so.
The problem remains there must be a drive letter assigned to the partition for it to be seen in Explorer. What exactly happens when you rightclick on it with Disk Mgmt to Assign/Change letter?
If this fails try free Partition Wizard installed version.
If this issue persists I would wipe the HD with Diskpart (to clean the boot sector of possible corruption) then clean reinstall following these steps to get a Perfect Reinstall.
SSD - HDD Optimize for Windows Reinstallation