I have a Dell Dimension 4100 and when I try to start the screen is black. It says that there is no signal. What do you think the problem is?

....and lights C, D are green, and your computer fails to boot up ? (you do not say) (on Dell PCs, which I don't have, the LEDs are usually described as yellow and green. There are four of them on rear of the PC ?).
First go to this webpage:
Product Support
if you are able run the Dell Diagnostics, or if not the ePSA.
Also read this manual - the only one available specifically for Dimension 4100 -
http://downloads.dell.com/Manuals/all-products/esuprt_desktop/esuprt_dimension_desktops/dimension-4100_Service%20Manual_en-us.pdf especially the section on safety. If you have to open the case remember to properly earth yourself.
To the answer to your question, if the 4600 model has the same codes as the 4100 see the service manual for the Dimension 4600 (or get the corresponding manual for the 4100 by contacting Dell support) look here
http://downloads.dell.com/Manuals/all-products/esuprt_desktop/esuprt_dimension_desktops/dimension-4600_service%20manual_en-us.pdf
in the Advanced troubleshooting section. It tells you the problem may be with your memory module(s) and it suggests what to try. I favour checking to see if you get correct errors with no memory inserted then with each module in each slot until all 4 combinations have been exhausted. This likely to tell you what is wrong. You may have to replace a memory module, or work with only one module or replace the motherboard.

23.June.2015

APB1963,
You can click the link below to download the online manual for the Dimension 41000. Within the manual are instructions for opening the computer case.
Dimension 4100 Online User Manual
http://dell.to/16xh0kC
Thank You,
Dell-Jesse L
Dell Social Media and Communities

No running system or Hard drive Failure

If this is all you see when booting it can be may things. CPU,Motherboard, RAM issues. Are you hearing beeps? if so how many? This will usually tell you what the issue is.

it means that the monitor is not receiving any signal from the cpu, check the cable that goes from the tower (cpu) to the monitor

your ram is prolly going bad

try to download and run "memtest86"

Do you have the software disks that came with the system? If it was given to you and you arent really sure of whats on it (viruses included), its worth reformatting.

If you have the disks, you can put the operating system disk into the computer and have it boot off of that.

if your num lock key responds, you may have to reseat/change the video card (if you are sure monitor is good). else you need to replace your motherboard.
Getback if you need any clarifications

First put the hdd installation cd into the cd drive and try to boot. This should install the hdd driver as well as start formatting the new hdd. After the drive is formatted take out the hdd cd & insert the Windows installation cd into the drive. Boot. Windows should start installing on your new drive. After Windows is installed check the Dell support site for updated drivers for your system. Install drivers as needed. Any other software you had on your old drive will need to be reinstalled to the new drive. Hope this helps & please rate my answer. Thanks.

maybe your dell dimension needs an audio driver. you can find drivers here by inputing the model or the service tag number. service tag found at the back of your PC.

http://support.dell.com/support/downloads/index.aspx?c=us&cs=19&l=en&s=dhs&~ck=mn&SvcTag=&SysID=DJ_DIGITAL_MP

Just follow instruction if your were in the site.

if this not solve;
try another audio card.