DELL 6400 Problem

Here's the basic description of the problem: sometimes (now, almost every time) when I try to power up my laptop, instead of turning on, the power light comes on, the battery light blinks rapidly but is faint, and the lock keys also blink rapidly and faintly. I can also hear a light tapping that goes with the blinking lights. Eventually, I can restart the computer by either a) forcing the issue by holding the power button down (this sometimes works) or b) just waiting long enough (approx. 20 minutes or more).

I know that there have been many threads about various models of dell laptops that won't start. I have contacted Dell support about the problem and followed their various steps to try to fix this issue (unplug everything, take out the hard and optical drives, reseat memory, etc). The laptop started just fine the time I was with support, but I think that was because I simply waited long enough.

Now I am left wondering: is my laptop doomed? Those of you who wrote in about similar problems, did your problem start like mine--first occuring once in a while, then almost every time--eventually leading to complete failure?