Inspiron 1501 - video failure, now won't POST

A while back, my mother started complaining that her Inspiron 1501 would no longer send video to her external monitor, and asked me to check it. Before I could get to it, the laptop's LCD also stopped showing anything, but she said she could still hear it boot into Windows.

Now it's not even reaching the initial POST -- hitting the power button causes the power icon to light up, fan spins briefly, hard drive seems to be on (but inactive), and the optical drive makes a momentary sound...and then it just sits there in total silence.  Tapping the power button again turns it off instantly.

So far, I've tried these without getting any results:

• booting after it has been plugged in for 12 hours
• booting without the battery
• holding down the power button
• removing the hard drive before booting
• booting after it spent 20 min. unplugged without the battery
• booting while holding Fn down
• booting while holding keys that usually go into other systems' BIOS (delete, F8, etc.)
• removing both memory sticks then booting
• starting with a Linux live CD, then with a Linux liveUSB plugged in
• combinations of the above

I'm not used to working with Dell systems, so I'm going by what has worked on other laptops and ideas I've found on various sites/forums, but at this point I'm at a loss.  Does anybody have any ideas for what to try next, or what could possibly have gone bad on it?