"Login with Ajax problem" is a vague topic and you'd get a better response if you were more specific.
I'm not sure what wordpress weaver is but if installing this plugin created a page with "%%Login-Form%%" then perhaps there's incompatibilities. You can't add that shortcode to a wordpress page within the dashboard and have it show - that text area is for content (not code other than HTML).
If your theme supports widgets, visit appearance > widgets and drag the ajax login widget to your sidebar and it should appear there. If you forums have that same widget area, it will show there too.
You can read more about the shortcodes and templates here:
But you may need to read more about theme development and widgets from this page if you don't understand the last link or need to install widgets for your current theme.