|There is no usable "My Computer" in Windows 7 - it has something similar - Computer.|
("My Computer" only shows up in Vista or Windows 7 if you change your Folder Options from their defaults and enable showing
hidden files and folders and possibly also enable showing protected operating system files and it's not usable like it was in XP and previous - it's there only for backwards program compatibility.)
The hard drive has to be software partitioned - using the FAT, or FAT32, or NTFS method - and formatted - in order for partitions on it to it to show up in My Computer in Win 9x to XP, or Computer in Vista or Windows 7.
If it's been wiped of data or if it's partition(s) has (have) been deleted, it won't show up in My Computer or Computer, or Windows Explorer.
If it shows up in Device Manager, that indicates the mboard's bios is detecting it, and it should also show up in Disk Management.
Control Panel - set it to display as Large icons or Small icons - Administrative Tools - System Management - Disk Management.
If it shows up in Disk Management, you can RIGHT click on the unallocated drive space on it to make one or more partitions and format it / them, then the partition(s) on it will show up in My Computer or Computer, and Windows Explorer.
If the drive has NOT been wiped of data and if partitions on it have NOT been deleted, something else is wrong.
In that case you need to provide more info about your " HDD docking satation "
If it's connected via USB, it must be connected to a USB port that can supply 500ma of current (amperage) and it may not work in the USB port you try it with in any case.
Troubleshooting USB device problems including for flash drives, external drives, memory cards.
See Response 1: