You may find yourself in a sort of "catch-22" if the only browser on your system won't work. If the browser keeps crashing upon launch, you can't really do anything to fix it, and in order to get an alternative browser you'd need to download it -- using a browser. Here are a few things you can try to fix your current browser, and there's even an alternative way to obtain a different browser without using a browser:
1. The first thing to try is clearing the cache and resetting the browser. Go into Control Panel > Internet options > Advanced > Reset Settings/Clear Cache. You will lose your bookmarks and cookies, but it may fix it.
2. In Add/Remove programs there's also a "REPAIR I.E." function. This may restore IE to a working condition.
3. You can download a copy of Firefox through the Windows command line using FTP. You can find detailed step-by-step instructions on how to do this at http://www.mattsilverman.com/2009/06/how-to-download-firefox-without-a-web-browser.html