In other Dell Systems, your beep code means...
This means that this note about beep codes may apply in some Dells, but may not apply in all...
the 2-2-1-1 reference that I found was for a Dimension™ 900 which is NOT your system!
http://support.dell.com/support/edocs/systems/dcaydim2/codemess.htm#post_beep_codes
Again, though, it points to memory. Memory, like all hardware, can fail.
If you do not have one already, get your owner's manual here,
http://support.dell.com/support/edocs/systems/dim4600/en/series_en.htm
There are two different versions of your computer, one with integrated graphics, and the other with an installed graphics card.
The manuals differ and the page numbers differ.
This is something you can learn to do... although
if you are uncomfortable doing it... your local tech shop would be glad to have your business.
They might even provide some education in the process.
Read carefully, and understand the dangers of Static Electricity and How to avoid damaging your computer.
Note also how the memory modules are secured.
You will need to Carefully release them, and then reinstall them.
Note which slot is primary, and install only one at a time, initially, to see if the problem can be isolated to one module.