Go to Start --> Run --> Type in iexplore about:blank
If IE starts it is the website you have set as default that is causing a problem on start up. Sometimes hackware and crap changes your home site to something not quite on the up and up. If your IE does come up go to Tools --> Internet Options --> General tab --> Home Page setting --> if the site listed is something normal that should work say www.msn.com or www.google.com or something then your install might be corrupt, if it is not and has been changed (possibly without your knowledge) than change it and save the setting. Once you do that you should be ok. Take note though that if your Home site was changed without your knowledge you either clicked yes when ya should have said no or you need to upgrade the security of your IE.
good luck