Well, let's forget (for a while) about the fact that it works in PowerArchiver - it is are not so important

, and also about the fact that avast! is the first item in the menu.
(More interesting question would be: are the usual items moved down in the context menu, or are they simply missing?)
Does the problem affects .zip files only - or would it occur e.g. with some other archives (.rar, .cab, ...) as well?
Check the default value of
HKEY_CLASSES_ROOT\.zipin your registry; it has some name (maybe CompressedFolder, maybe ZipFile, don't know).
Now, navigate to the key called exactly the same under HKEY_CLASSES_ROOT
(e.g. HKEY_CLASSES_ROOT\CompressedFolder).
What's the content of the "ShellEx" subkey (especially ContextMenuHandlers key)?