when trying to open a TextEdit file or just to launch TextEdit, the "TextEdit quit unexpectedly" window appear.
It's possible you're running an outdated version of TextEdit, which because it is tied with the OS could also mean your OS is outdated. What OS version are you running (on the desktop click the Apple in the upper left hand corner and click on "About this Mac").
Assuming you're running at least 10.5, that latest 10.5 is 10.5.8, and the latest 10.6 is 10.6.8. Have you tried running "Software Update" (on the desktop click the Apple in the upper left hand corner and click on Software Update) to make sure your OS and all its integrated components, namely TextEdit, are up-to-date? The current version is 1.7 build 288 released in July.
iMac G5 1.8GHz "Hero" PowerPC
2 x 1GB DDR PC3200 SDRAM
160GB WDC WD1600JD-40GBB2
Mac OS X Leopard Version 10.5.8