Sometimes advertisements will pop-up windows and turn off these bars. I think they do this so that you can't manipulate the window or easily block them. So, it might not be spyware, but just the advertising jerks and their pop-up ads. It's very annoying, but it happens.
Anyway, since I don't know which IE you are using or your OS version, I don't really have a compact solution for you; however, I did look up "address bar missing how to restore" in an advanced search at the microsoft support website at http://support.microsoft.com
and here is a webpage that I found:http://support.microsoft.com/kb/942172/en-us
This was for IE7 on Vista. I'm not sure if it addresses your problem, but it's a solution for that configuration. It goes through changing registry entries (which can be dangerous if you're not careful or don't know what you're doing).
I know there is a reset button on the Advanced tab of the Internet Properties. Since you don't have an address tab, I don't know if you have a menu bar either (they are separate bars). If you have a menu bar you can access the "Internet Properties" by selecting "Tools" on the menu bar and selecting "Internet Options" near the bottom of the menu. When the Internet Options popup dialog appears, select the "Advanced" tab and at the bottom of that page there is a button labeled "Reset..." under "Reset Internet Explorer settings". This will reset everything on IE to default settings (disables add-ons, etc).
If you don't have the IE menu bar, you can bring up the control panel (press the red Start button and select the Control Panel).
a) If it shows "Pick a Category" then choose "Network and Internet Connections" and then "Internet Options".
If you don't see "Pick a Category", but you see a bunch of icons, you're in the "Classic View" of control panel and you will want to look for the icon that is named "Internet Options".
Click on the Internet Options. You will see an "Internet Properties" pop-up window that will have tabs across the top. Select the "Advanced" tab and you should see the same "Reset..." button as was described above in IE7.
I hope this give you some information to go on.