Not posting the model number of the Dell desktop computer, get's you generic information.
The model number can be found on the back of the computer, next to the Windows product key.
Suggest use an external enclosure.
Remove the harddrive from the computer, and install it in an external enclosure.
The external enclosure has a USB cable, and you just plug it into any available USB port, on a working computer.
Then go to My Computer, or Computer; depending on which Windows operating system the computer has; and double-click on the drive letter that corresponds with the external enclosure.
(WinXP: Start > My Computer
Win Visa / Win 7: Windows logo button > Computer )
Examples of drive letters;
C: Drive = Harddrive of the computer you are using
D: Drive = Separate partition on the harddrive for Restore files, or is for the optical drive (CD/DVD drive)
E: Drive = Optical drive generally, but may be the drive letter that corresponds to a Removable Device.
The external enclosure you plugged in, is a removable device.
None of the above is 'etched in stone', except the C:Drive
Things change from computer to computer, and the way you may have it set up.
Easy way to know?
Before plugging in external enclosure, open My Computer, or Computer.
Look at what each drive letter corresponds to.
Now when you plug the external enclosure in, you will see the change; and know which drive letter corresponds to the external enclosure you just plugged in.
Double-click on the name next to the drive letter, that corresponds to the external enclosure you plugged in.
Go into My Documents, or Documents.
Again, depends on which version of Windows you have.
Win XP = Start > My Documents
Win Vista / Win 7 = Windows logo button > Documents
Now open each folder, until you get the personal files you want to keep.
Photos, music, videos, documents you have created, or downloaded.
You cannot remove programs, or applications. Just your personal stuff.
(You can, but that is for a separate discussion)
Also open Downloads.
(WinXP = Click on Start > My Documents > DOUBLE-click on Downloads.
Win Vista / Win 7 = Click on the Windows logo button (Start), click on Documents, click on Downloads.
Harddrives are measured in Width.
2-1/2 inches across for a laptop harddrive. 2.5 inches.
3.5 inches for a desktop harddrive.
Don't know what Dell this is again, don't have the model number.
Cannot tell you if the harddrive is an IDE (PATA) unit, or a SATA unit.
So you will need either a 3.5 IDE (PATA) external enclosure,
a 3.5 SATA external enclosure.
There are external enclosures that are 3.5 and IDE/SATA, also.
Easy way to identify what type technology is used, for the harddrive in your computer; IDE/PATA, or SATA;
Power cable for an IDE/PATA harddrive,http://www.playtool.com/pages/psuconnectors/connectors.html#peripheral
Power cable for a SATA harddrive,http://www.playtool.com/pages/psuconnectors/connectors.html#sata
For additional questions please post in a Comment.