Okay, this one's a poser.
Got a 3-year-old Inspiron 1546 - actually I have two identical ones from the same customer with what appears to be the same problem. It won't start up.
When I press the power button, the power light lights, I get a humming sound, and the system fan starts - all good so far. Then the fan immediately loses power and spins down after about 4 seconds. After 15 seconds of humming, everything stops and the power light goes off.
Whether the laptop battery is in or not doesn't seem to matter. I tested the RAM, hard drive and power adapter in both PCs, all of which were OK.
I then replaced the coin battery in one of the PCs with a new one, and got a change in behavior: The process detailed above repeats as a cycle. At the end of 15 seconds, the power light blinks, there is an audible clicking sound, and the process starts again. The cycle then repeats itself indefinitely. (I only did this to one of the laptops because Dell, in its infinite wisdom, requires one to tear the laptop apart to replace the bleeping coin battery ... Sigh.)
After 15-20 of these cycles, I got another change in behavior - the automatic repetition stopped. The system now goes through a single cycle, like it did in the first place, and then powers itself off.
It looks to me like the fresh charge in the coin battery was being used to keep the cycle repeating until it drained. It does not appear to me that the system is getting enough power to boot.
I've done a lot of web research and haven't come up with anything except a possible issue with fractured pins in the CPU (http://www.hardwareanalysis.com/content/topic/43678/), though that was with a different model of Inspiron.
Any ideas? Thanks in advance.