The disappearance of IE could very well be related to your malware issues.
Because you have a log posted here: http://www.bleepingcomputer.com/forums/t/209770/uacrootkit-detected-on-my-laptop/ you should NOT make further changes to your computer
(install/uninstall programs, use special fix tools, delete files, edit the registry, etc) unless advised by a HJT Team member, nor should you continue to ask for help elsewhere. Doing so can result in system changes which may not show in the log you already posted. Further, any modifications you make on your own may cause confusion for the helper assisting you and could complicate the malware removal process which would extend the time it takes to clean your computer.
From this point on the HJT Team should be the only members that you take advice from, until they have verified your log as clean.Please be patient. It may take a while to get a response because the HJT Team members are EXTREMELY busy working logs posted before yours. They are volunteers who will help you out as soon as possible. Once you have made your post and are waiting, please DO NOT make another reply until it has been responded to by a member of the HJT Team. Generally the staff checks the forum for postings that have 0 replies as this makes it easier for them to identify those who have not been helped. If you post another response there will be 1 reply. A team member, looking for a new log to work may assume another HJT Team member is already assisting you and not open the thread to respond.
If after 5 days
you still have received no response, then post a link to your HJT log in the thread titled "Haven't Had A Reply In Five Days?
To avoid confusion, I am closing this topic. Good luck with your log.
If you are still experiencing issues with a vanished IE once the HJT team has declared you clean, then send a PM to a moderator to reopen this topic.