Whether I am using just the battery or have the power supply plugged in, when I turn the power on, the windows XP system does not load.  Instead, the computer starts to load - with a black screen - and then shuts off and repeats this over and over and over until I either take the battery out or unplug the power supply cord.

If I leave the battery in - it keeps trying to load then shuts off again and again.  I guess it would KEEP doing that until the battery was dead. 

This is a laptop?

How old is it, and what is its model number?It is about 3 years old.  The model number is PC - 434421 A  or maybe m5500i-R3?

I should ALSO include that I took the back off just to check where the wireless card was because the internet kept going on and off before this other thing started happening.  It didn't start shutting off and turning back on until after I put the back on.  I really did not do anything to any of the cards.  I just looked at it.  I did notice that the fan was not turning on right away.  Does it wait until it gets hot enough first? 

Is it by any chance still under warranty?

When you removed the back of the laptop, what is there? What hardware is visible?
If you cannot name them, feel free to post a PICTURE(s).

You may have accidentally hit something loose.I am having a similar problem with a presario Compaq laptop. model v6000. I at first had to remove the battery then replace it before it comes on. Then I started cleaning the memory card. it only worked for a Short while then it just when on the way you DESCRIBED.
 I am still searching for a solution.