Q: Clean Cache

Welcome to the Apple Support Communities

To repair permissions, just open Disk Utility, select Macintosh HD in the sidebar and press the button to repair permissions. You don't have to clean caches.

To clean caches, the best way is to start into safe mode, so cache will be deleted automatically during startup > http://support.apple.com/kb/ht1564

You can ignore all of those permissions because there isn't any problem with them > http://support.apple.com/kb/TS1448

Mac OS X: Disk Utility's Repair Disk Permissions messages that you can safely ignore

Start by explaining the problem you are experiencing that led you to the following assumption

I assume that Some running ermissions got corrupted ...

Because my Safari Browser First slowed Down so I did a restart but the Screen went grey and stopped booting. Did all recommended Apple Support advices but only Start and re-install from OSX Disk worked but still Safari is Slow as before and Even Runs endless without opening any Homepage.

If you have not already done so, back up your Mac since those symptoms may indicate a failing hard disk drive. It can be replaced, if necessary.

Start your MacBook using its original System Install DVD and run Disk Utility. Repair the disk. Report any errors it finds.

Good. Are you using OS X 10.6.8?

To find out go to the Apple menu and select About This Mac. Please report what it says next to each of the following:

Version

Processor

Memory

Go to Safari menu > Safari Preferences > Extensions. What do you see there?

dieleffe wrote:

 

Not Sure why u had ASK that question since clicking on extentions Opens link to install them.

That would seem to indicate you have not installed any extensions.

I concur that this sounds like your hard drive is failing. Use SMART Utility for Mac demo to check it out.

For some ideas on browser slow downs, see Macintosh OS X Beachballs! from Randy Singer.