Data recovery from External HDD

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Hello all you wonderful people!

Background
I have a Western Digital 300 GB HDD and a PC with specs as follows:

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More details about my computer


Component Details Subscore Base score
Processor Genuine Intel® CPU T2300 @ 1.66GHz 4.1 2.8
Determined by lowest subscore

Memory (RAM) 3.00 GB 4.6
Graphics Mobile Intel® 945 Express Chipset Family 2.8
Gaming graphics 256 MB Total available graphics memory 3.1
Primary hard disk 14GB Free (37GB Total) 4.1
Windows 7 Ultimate

System
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Manufacturer Dell Inc.
Model Latitude D620
Total amount of system memory 3.00 GB RAM
System type 32-bit operating system
Number of processor cores 2
64-bit capable No

Storage
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Total size of hard disk(s) 969 GB
Disk partition (C 14 GB Free (37 GB Total)
Media drive (D CD/DVD
Disk partition (E 856 GB Free (931 GB Total)

Graphics
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Display adapter type Mobile Intel® 945 Express Chipset Family
Total available graphics memory 256 MB
Dedicated graphics memory 0 MB
Dedicated system memory 64 MB
Shared system memory 192 MB
Display adapter driver version 8.15.10.1930
Primary monitor resolution 1440x900
DirectX version DirectX 9.0 or better

Network
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Network Adapter Broadcom NetXtreme 57xx Gigabit Controller
Network Adapter Intel® PRO/Wireless 3945ABG Network Connection
Network Adapter Virtual Machine Network Services Driver
Network Adapter Virtual Machine Network Services Driver

Notes
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The gaming graphics score is based on the primary graphics adapter. If this system has linked or multiple graphics adapters, some software applications may see additional performance benefits.
Caution: Based on the results of the WinSAT Disk assessment, your system drive may have slower response times under some workloads. Performance results will depend on the specific applications used and the amount of memory available. If your experience is satisfactory, no action is needed.

Problem

I cannot access the data on my HDD because there is no assigned drive letter. I need to access the HDD. It is not showing up in explorer.

Notes

• My HDD does not show up in explorer.
  
• It shows up in Computer Management with out a drive letter.
  
• The option to assigne drive letters and paths is greyed out.
  
• I believe the cause of the problem is that someone did not eject the HDD before unplugging it.
  
• I am recovering data with large file sizes. (Videos & final cut projects.)
  

Any help would be greatly appreciated. Guidance to a program that will solve my problems would also be great. Let me know the name of the program and I will go and download it from the manufacturer's website after paying for it.