What is your actual website URL?
That type of link you are showing is how Core Joomla! makes links in your site. I got a site running Joomla! 1.0.x with JoomSEF installed + Joom SEF Patch Extended and I have no problem with links on my site. Check them out here at
www.kaufman-ares.org/latest/2008-ares-cert-scholarship.html
I also use JCE for my WYSIWYG editor and it has an item included that makes it easier to add both external link and internal links with out much work. In fact on the internal links it allows to to get your link into your page by choosing what type of content its, ie. static, file, sec/cat, etc. and you choose the item and it handles inserting the link, then JoomSEF provides a correctly formatted link to where it goes, both on the surface, of the page, if you use the link also as the wording or link certain words (normal links) the source code and the destitation on hover show just where its supposed to go.
I am still fairly new to all of this, but if you need help, please feel free to contact me and I will see what I can do for you.