I am also having the same problem with my four year old Inspiron 600m (purchase November 2004). Sometimes the notebook powers up just fine. But most of the time, when I push the power button, the three LED's (cap lock, num lock, and scroll lock) will blink quickly for about five seconds and then nothing. I've tried booting from the battery (freshly charged) and removing the battery and running only on AC. I've also tried re-seating the RAM chips, the CD-Drive, and the hard drive. So far, nothing has worked. The problem seems to be getting worse and I have backed up my data -- but I'd like to continue to use the notebook computer. In its current state, I just don't have confidence that I would be able to turn it on when I really need it.
Has anyone ever hear of a realiable diagnosis for what would cause the three LED's (cap lock, num lock, and scroll lock) to blink quickly for five seconds at power up and then nothing happens? I've seen speculation that it is a motherboard problem, but nothing beyond that.