so my main power cord going into the socket and the back of my Dell Latitude D600 Windows XP and my batter icon on the side of my computer system is blinking red and green. So, does anyone know how to fix this I really don't have the money or time to go and take it somewhere. So anyone?

Does it turn on?
Sounds like a power problem.
To troubleshoot the power;
Try it without the battery installed.
Try a new power supply, with out the battery installed.
Try it on battery only.

If none of that yeilds any result you may have an internal power issue, in which case you would need someone to take it apart and inspect the board for problems.

yes it's plugged in. But the battery is low and needs charging. The battery charging sign thingy that's located on the bottom right of my laptop is blinking both green and red. and the power source says charging but it's not changing, it keeps says '0%'

A bad battery can cause this type of behavior. If you can't get access to a battery (maybe a local batteries plus store could help) or power adapter to test it then you'll likely have to pay some one to troubleshoot it.
Batteries on Ebay
Power Adapters on Ebay