I agree. Cold booting to safe mode (pressing the <F8> key repeatedly once per second as soon as you press the on button will usually be a good test. You should get video on the screen at a very low resolution... but the screen should stay on. If this is the case, it is likely your video connection needs the drivers reinstalled, or the video card replaced.
What is the model or Service Tag from the back of the computer?
The usual other cause is a failed hard drive. Most Dell desktop and laptop machines will give you the flash screen... e.g. the Windows Logo and related first startup screen. It is generated from the motherboard set. Once that Windows Logo starts up, it wil then switch to the hard drive. If the hard drive is failing, it will quit at this point. The Windows XP screen goes away to black, and nothing else happens.
If it is under warranty, you need to talk to Dell next. If out of warranty, come back to us for more ideas.