Dell Latitude won't boot

I have a Dell Latitude C610 that won't boot. When I press the power button,
the three lights at the top of the keyboard all blink once at the same time.
The screen has one white flash then remains dark. The power light at the
right of the keyboard comes on. The hard drive light comes on briefly and I
can hear the hard drive begin to spin. Then it shuts down. All lights go
off. It never gives any message on the screen. No evidence of POST. When
I put the floppy drive in with a boot diskette, it will act like it is
trying to read the floppy, then shut down the same way. Nothing ever
appears on the screen. I have taken the battery, floppy, and hard drive out
and tried to power up with just the power adapter and get much the same
results. I have made sure the memory is installed properly. I have taken
one memory stick out and tried it one at a time with the same results. I am
reluctant to start buying parts without knowing which part is bad. What
should I try next?

Thanks