YES, Zian it will work....BUT,....................
1) It is a PCI graphics card, and uses a PCI expansion slot.http://www.tigerdirect.ca/applications/SearchTools/item-details.asp?EdpNo=2898922&CatId=319
The Dell Dimension 2400 Desktop PC's motherboard, has three long white PCI slots,http://support.dell.com/support/edocs/systems/dim2400/en/sm_en/techov.htm#1105465http://www.ebay.com/itm/Dell-Dimension-2400-Desktop-Motherboard-System-Main-Board-F5949-K5148-G1548-/190750417467?pt=Motherboards&hash=item2c699c623bhttp://en.wikipedia.org/wiki/Conventional_PCI
If one of those long white PCI slots is open, you can use a PCI graphics card.
Concerned that the graphics card uses DDR3 graphics memory, and your computer only uses DDR Sdram ram memory?
The graphics card has it's own processor (Graphics Processing Unit), and graphics memory.
It runs independent of the system resources; the Processor and Ram Memory.http://en.wikipedia.org/wiki/GPU
The concern is the Power Supply.
Original power supply's maximum rated Wattage is either 200 Watts, or 250 Watts.
The above graphics card requires a minimum system requirement/power supply requirement; of 300 Watts.
I would recommend replacing the Power Supply.
(Especially with it's age, if it is still the same one)http://www.tigerdirect.ca/applications/SearchTools/item-details.asp?EdpNo=1389575&CatId=1078
ONE thing though..............
Watch the 20-pin ATX main power cable connector, and the wires in it. Be sure they are in the standard place setup.
Check the pinout, and color code of the wires,
1) Dell Dimension 2400 desktop computer, 20-pin ATX main power cable connector pinout,http://support.dell.com/support/edocs/systems/dim2400/en/sm_en/techov.htm#1105612
2) STANDARD 20-pin ATX main cable connector pinout, and color code of wires; as set by JEDEC,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
[Be aware that the ATX main power cable, and connector, you get with a new power supply; such as the above, will have a 20 =4-pin ATX main power cable connector,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20plus4
Use the 20-pin connector, tie the 4-pin power cable up out of the way]
For a time period Dell was making the motherboard's main power cable connector - Proprietary.
Meaning they has that motherboard connector wire pinout changed.
Colors of wires were in a different place, than the standard setup by JEDEC.
Orange wires are 3.3 Volts (DC)
Red wires are 5 Volts (DC)
Yellow wires are 12 Volts (DC)
Black wires are Ground wires.
Guess what happens if a 12 Volt Yellow wire, is plugged into where a Black Ground wire is supposed to be?
ZZZZZZzzzzt! Motherboard fries, processor fries, ram memory fries, and graphics card. (If used)
Check the color code of the wires, in the 20-pin ATX main power cable's CONNECTOR, for the Dimension 2400's power supply.
For additional questions please post in a Comment.