System is the process manager for the kernel and handles low level runtime operations, er, short form is no you can't shut it down (you can't anyway because it runs at a protected level, give it a try).
System Idle is actually sort of a non-process - when nothing else is going on, the idle handler *should* report a high %.
The procs you have to look out for are svchost.exe - these are service wrappers for like DLL's that can become massive cycle hogs (and are a good hiding place for virus's and other malevolent apps).
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Try a freeware called cCleaner to clean up your registry and files on computer.