In general, troubleshoot NetBeans issues by using the View > IDE Log command. You should see Java exceptions there related to the IDE. You can also view them in a file at $HOME/.netbeans/6.7/var/log/messages.log.*
It is possible that a NetBeans plugin you have installed has corrupted NetBeans configuration and is causing the problem. One way to test this is to remove the $HOME/.netbeans folder (while the IDE is closed) and let NetBeans rebuild it by starting the IDE.
Finally, you can uninstall NetBeans (by using the uninstall.sh script/JAR in the NetBeans installation folder.
Also, do recall that Ctrl+Space is one way to invoke suggestions; the other (for markup) is to type the < (less-than) character.
Although NetBeans has a verifiable historical problem with XML-related code completion, the 6.7 release should work as expected. Just be careful with installing a bunch of crazy plugins!