As I'm sure you are aware a CD/DVD drive is a mechanical device. It's 'lifespan' is rated in hours of usage. With the C521 being 4 years of age, I wouldn't think the DVD dual-layer burner drive would be defunct. Does depend on how much it's been used.
Ordinarily I would state cleaning the optical eye in the CD/DVD drive, and also reinstalling the drivers, if a disk is not recognized. However the, " Computer does not recognize it as a drive.", statement concerns me.
Suggest you try the software approach first of reinstalling the drivers, then if you wish go on to the hardware approach, of checking to see if the data, and/or power cable is loose on the DVD drive.
Reinstalling the Drivers:
The main method;
1) Left-click on Start
2) Right-click on My Computer
3) Left-click on Properties at the bottom of the list
4) Left-click on the Hardware tab
5) Left-click on Device Manager
6) In the Device Manager list, left-click on the + sign next to Disk Drives.
7) Now right-click on the name of the DVD drive.
Here you will have the options of either Uninstall, or Update Driver.
I suggest you left-click on Uninstall.
Update driver seldom works.
A warning will come up, "Warning you are about to uninstall this device, ya-da, ya-da"
It's okay. Click on OK.
Close all windows, go back to your desktop screen. Shut your computer down normally. (Start > Turn Off Computer > Turn Off)
Wait 1 minute, turn your computer on.
After Windows has loaded you should see a pop-up out of your system tray, "Found new hardware".
Plus perhaps another one, "Found XXXX DVD writer"
Then it's time to check the above mentioned cables.
Your Dimension C521 uses a SATA optical drive. (DVD drive)
The Data, or Interface cable looks like this,http://en.wikipedia.org/wiki/File:SATA_Data_Cable.jpg
(The color of the cable may not be the same, and it may not have a 90 degree elbow connector)
It is a 7-pin connector.
Make sure it is plugged in tightly to the back of the DVD drive, and also to the SATA header on the motherboard.
BEFORE you reach inside your computer!
Computer unplugged from power, observe Anti-Static Precautions.
Your body carries Static electricity.
Static will Fry Out (Short Circuit) the hardware components inside a computer.
Computer unplugged from power, working on a table, open the computer case.
TOUCH the metal frame of the open computer case, to relieve your body of Static.
Should you get up, an walk away in the middle of working on your computer, upon your return be SURE to touch the metal frame again.
Computer unplugged from power, you're safe. TOUCH the metal frame of the open computer case, your computer is safe.
Here is a link to Dell Support, and the Service Manual for the C521,http://support.dell.com/support/edocs/systems/dimc521/en/SM_EN/index.htm
You will see - Removing the Computer Cover, and Replacing the Computer Cover.
In the main menu list you will also see - Technical Overview.
If you click on this heading, and then on - System Board Components, you will see the motherboard in an illustration.
Here you will see the Ram Memory slots. Below them is where the 24-pin ATX main power cable plugs in, (No.5), and to the right of the main power cable are two SATA headers, on the motherboard. (No.6)
Your SATA harddrive plugs into one of these SATA headers, and your DVD burner optical drive, plugs into the other one.
The SATA power cable going to your SATA DVD burner drive, comes from the Power Supply. It's a 15-pin connector. Looks like this,http://en.wikipedia.org/wiki/File:SATA_power_cable.jpg
Be sure it's plugged in tightly to the DVD burner drive.
It could be a bad SATA Data cable.
More than likely your DVD drive is just toast. Seen the last of it's days.
Your Dimension C521 uses a regular size SATA DVD burner drive, even though it's a Slimline style of computer.
There are MANY drives available, should you decide to replace it.
You can also use one of these drives in an external enclosure. This way you just plug it's USB cable, into any available USB port on your computer.
If I were to recommend a SATA DVD burner drive, I would recommend one of the Lite-On models.
Cost less than most, but have features, and reliability of those that cost 3 to 5 times as much!
I'm using a Lite-On model that cost $48 from a large store, but could have purchased it for $28 online.
It's a DVD SATA burner drive that will support dual layer disks, and has LightScribe Technology.
Has lasted over 4 years now, and a clients computer that I installed the same model, has lasted over 5 years now.
(I see they're cheaper now, sheesh!)
Barring you do not wish to open your computer, and replace your DVD burner unit, here is an example of a 5.25 SATA external enclosure,
(A laptop harddrive is 2.5 inches across in width. 2 and a half inches. A desktop harddrive is 3.5. An optical drive is 5.25 inches. 5 and one-fourth inches),http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=2414551&CatId=2784
If you have any questions please post them/it in a Comment.