First confirm if its really a NO POST issue. Meaning it fails to Self Test. One quick way is to toggle the Caps Lock Key while in this state. If the caps lock light turns on, your computer appears to be posting ok.  If it doesn't, you're gonna have to do something else.

Reset the system. Take the battery out and disconnect the AC adapter. Hold down the Power Switch for about 30 secs without power. This should clear the NVRAM, so to speak.

Check the memory. Reseat the mem sticks if you may, then try again. That usually helps.

ALSO>> Check the Power Source. Maybe your not getting power! Check the green light on the AC adapter if its steady green.  Also check your battery charge indicator on the battery itself.  Maybe your just out of power. ( Sometimes the charger board on this thing cuts out. Leaving you with no power for the system and no power to charge battery).

Among other things.....

I think you should first connect it to an outside monitor.  It may have started and the screen is not functioning.  Seems to be an aggravatingly common problem.

Bill

I'm having the exact same problem with my i8200, which is 1 1/2 years old and out of warranty.  I've tried all sorts of suggestions, including taking the laptop completely apart and re-seating virtually every internal component, using the Dell Reinstallation CD, etc. 

Has your home recently lost power or had any electrical problems?  When I came home one day last week, my digital clocks were flashing, and from then on I've been having this problem with my laptop. I'm not sure if it was a surge or outage, but my laptop was plugged into a wall outlet via the AC chord with no surge protector, so that may be what caused my problem.

And here's what's really maddening: My laptop does what you describe about 98% of the time (pressing power button, LED lights come on for 3 - 4 seconds, then shuts off with nothing ever appearing on the screen), but when I repeat this process over and over enough times (I'm stubborn), my laptop will occasionally attempt to boot up.  This has led to various messages, blue windows, etc., most of the time.  Then a couple days ago it completed the full bootup process and I was elated, although my nVidia video driver was not found and an error message said that the default VGA driver was being used instead, so the desktop display was very poor quality with a huge black border.  I didn't care and frantically tried to burn some files which I desperately need from my hard drive to the CD-RW, but the laptop promptly froze up before I could start the process.  I rebooted it successfully a couple more times, but it would always freeze up after a few minutes.  Then it went back to what it had been doing before, and it hasn't even attempted to start the bootup process since then. 

Anyway, I've given up and have taken the laptop to a local PC repair place, since it's out of Dell's warranty.  I'll try to follow up and let you know what I found out, but the PC guy at the repair place didn't sound optimistic when I described the problems to him.  (I've used this place before and have full confidence in them).

What's odd is that, if something inside the laptop got fried by the electical surge, why does it occasionally boot up? You'd think it would be completely dead.  Makes me think it might be a virus, but who knows.