you could try using server side GA. which try to mimic the js script using php. this is the most fleshed out version I know http://code.google.com/p/php-ga/

For statistical purposes all the people with JS enabled should be enough; but just for the sake of the technical challenge: 1) Link position, if they clicked a link under the first 1000 pixels of the page they probably scrolled. 2) Something similar but more complex can be done with images on CSS hover effects (using the webserver access logs) BTW, using something similar to this together with the "media" attribute on LINK tags allows you to see witch CSS file they are using, and therefore screen resolution.