i had magento installed on my server working properly but now the manage category page is broken and i can't do anything in this page . i searched in forums and tried different solutions but they didn't work .
Either check the console or check the system.log or exception.log file. And if you find any error then try to solve that error.
If you have installed any custom module and after that you are getting this error then disable that extension.
When you say "the manage category page is broken" what exactly is broken? Are there any errors on screen? And as theMageComp suggests, check error logs.