Shut-Off, then Screen Problem on D630 Latitude Laptop

Recently I've been having a problem with my laptop computer;

Dell Latitude D630 laptop
Win XP Pro svc pk 3
Intel Core 2 Duo, 1 Gig mem, 120 Gig HD
DVD RW drive:  HL-DT-ST DVD+-RW GSA-T21N - Drive(D:)

I'll be working, then it freezes up with the mouse becoming unresponsive, the screen
may get this funny pinkish tinge to it at times, and then it just suddenly turns off/
loses power without fanfare. It does this both while running on external AC power, or
on the fully charged battery.

After this episode, it will appearently boot up normally, but with no screen display.
The screen is working (I think) because it is lit up, but just showing black, and it
IS booting up, because I can hear all the Windows tones and songs playing on the speaker,
both for start up and if I hit the power off button....I just can't see what is going on
because the screen is black, but lit.

This behaviour continues until I give up trying. The screen just stays black while the
computer boots, with the exception of one time, when it showed the Dell BIOS pre boot
screen before going black for the rest of the boot.

The screen may work the following day the very first time I start it up, until the computer
freezes and shuts off again, usually within the first 20 minutes or so. Then it's done
for the day again.

After reading an article here, I tried the following

Powered on while pressing the "D" key - nothing on screen, but got some tones from the
speaker during start up.

Powered on pressing the [Fn] key - 1st time - the screen finally lit up showing a bunch
of solid colors while giving a series of beeps, then it would "sing", then series beep,
then sing again, and it kept doing this until I hit the power off button again.

When I tried it a second time, the screen came on again and I got what it said was a
"Diagnostic Boot"???. It then ran a series of tests lasting about 45 minutes before saying
nothing was wrong.

But I didn't do anything. What is my problem, and how do I fix it? I can't have it
shutting down on me by surprize.

Thanks, Dave