Looking at the site I can see that there has been quite a bit of customisation, it's looking good.
The slider problem is probably a jQuery conflict caused by the additional code included by the plugins. The quick test here is to disable all your plugins, and activate one-by-one testing the slider to see which one stops it working. Or it could be a combination of 2 or more plugins conflicting when they're both active.
The "Site Awards" text widget appears to be outside of the sidebar (at least according to the source code) which suggest one of a few problems has happened:
1.) the widget was placed outside the sidebar area.
2.) a plugin has closed the #sidebar div because of a coding error and the next widget is on its own (you'll only be able to find out by disable / re-enabling one-by-one) - more likely because the widget was originally in the sidebar.
Something has changed if these problems have just occurred, if you added a widget / plugin or cleared your cache and a previous bug which was there (but hidden by cached files) has just surfaced check what may have changed or refer to a recent backup to restore the site functionality.