Abruptly cutting the power to your computer is not a solution to anything; it can cause serious damage to you, and put you at risk for electrocution. Stop doing that.
Time Machine is only for Mac OS X 10.5 and 10.6; it does not work with anything less, although if you have an external disk with 10.4 on it and it's connected to a Mac running 10.5 or 10.6, the Time Machine will back it up.
However, Time Machine is just not all it's cracked up to be. You can get better backups from any system by using third-party software, such as:
Carbon Copy Cloner: http://bombich.com/ or
SuperDuper: http://shirtpocket.com/