Are you it isn't a VGA cable?

If you are refering to the VGA technology:
"Many modern LCD-monitors support both the Digital (DVI) standard and the Analog (VGA) signal. If I'm not too wrong, your monitor included a DVI cable and a VGA cable, because older graphics cards don't support DVI. I assume your E510 came with at least a stock ATI Radeon x300, which has one DVI and one VGA connector, and since you have an Ultrasharp monitor, you won't have any use of a VGA cable, as the monitor is connected with the DVI cable".

Not sure what you mean. A VGA cable *IS* a standard monitor cable. Do you mean it came with both a DVI and a VGA cable? If so, use DVI if your system has a DVI port, otherwise use VGA.

I have a Dimension E-510 also, and I  have the UltraSharp monitor connected via (the white colored) DVI cable.... awesome monitor; I love it... If you do in fact have a DVI port, connect your UltraSharp with the DVI cable because the sharpness / clarity is  so much better than the (blue colored) VGA cable.