The lights you see flashing are Diagnostic Lights. These tell you of a possible area to look into for the problem.
Lights 3, and 4 flashing green, mean a possible Ram Memory problem.
I would like you to view the free Owners Manual from Dell Support, in the event that you do not have one.http://support.dell.com/support/edocs/systems/dime521/en/index.htm
This PDF document can also be saved to your computer, thereby allowing you to copy it to a CD disk. If you are not aware of how to do this, and wish to, simply state so in a Comment.
(After you burn this PDF file to disk, you can remove it from your computer, freeing up more space on your harddrive)
Where it states Owners Manual, left-click on View to the right.
You may also be interested in viewing, (And copying), the Service Manual.
What I would suggest to start.
1) Computer off, unplug your computer from power.
Working on a table, open the computer case.
TOUCH the metal frame of the open computer case.
This action will relieve your body of Static electricity.
Your body carries Static. Static will fry out (Short Circuit) computer hardware components.
(Should you get up in the middle of working on your computer, and leave, upon your return Touch the metal frame again)
Remove all ram memory modules. (Ram Module = Ram 'stick')
Use a pencil eraser, and clean the gold plated contact pins on the bottom of the ram module.
This is a photo of a basic ram module,http://en.wikipedia.org/wiki/File:Generic_DDR_Memory_%28Xytram%29.jpg
Here, you can see the gold plated contact pins I have referred to.
(Ram Memory used for the Dimension E521 Desktop PC, is DDR2 Sdram.
DDR2 Sdram has 240 contact pins. 120 on each side.
The photo is of DDR Sdram.
184 contact pins, 92 on each side)
If possible, it is preferred to hold the ram memory module by the body of the module, and refrain from touching the contact pins. The body of the ram memory module is covered by a see-through plastic.
Start at the top of each contact pin, and work down, using the eraser.
Remove the eraser dust with air, and reinstall.
If you have two ram modules, try inserting one at a time.
The ram slot closest to the Processor, is Ram Slot 1. (May be marked as DIMM 1 on the motherboard)
Ram memory should be installed in ram slot 1 first.
The Processor reads ram memory installed in ram slot 1 first.
In the Service Manual if you click on - Technical Overview in the main menu, then click on - System Board Components, you'll see where the Processor
is located, (2 - processor socket), and where the ram memory slots are, (3 - memory module connectors)
Removing and Installing Parts, located in the main menu also, will show, and tell you how to open the computer case, and how to remove, and install ram memory modules.
(Removing the computer cover. Memory)
Should you need more in-depth guidance of how to do the above, please state so in a Comment.
Should this not fix your problem, please state so in a Comment.