The 32-Bit or 64-bit has nothing to do with this issue. When an Administrator install any kind of software in your system, most software offers two types of Architures bits either 32 or 64. Your issue is vague. However, if you have already installed Java but Applets are not working in your IE browsers, then switch your browsers to Firefox or Chrome.
The Applets are not workinb in your system because you have installed Java but you haven't enabled Java. Go to Java control panel and enable it manually as per your preferences. I never use IE so I have no idea whether it supports Java or not. However, to see whether your IE supports Java, you need to see whether your browser is is out of date or need to update to latest version configured to use Java, check your settings in the Java Control Panel.
Please note that Im using Windows 8 64-bit since I don't prefer Windows 7. The setting and control panel for this tutorial might be vague for you. So make sure you follow the below steps systematically as per your system control center.
Step 1: Go to Control Panel>
Step 2: Java> Java Control Center>
You will find 5 TABS. Click on the fourth tab Labeled with SECURITY.
Step 3: Enable Java in Browsers
Step 4: Go to Edit List> Add IE, Chrome, Fire Fox etc... Whichever browser you want to enable Java contents.
Step 5: Hit the APPLY option> Ok> Restart your PC to affect the changes.
Second Solution for Internet Explorer:
Step 1: Click Tools and then Internet Options
Step 2: Select the Security tab, and select the Step 3: Custom Level button
Step 4:Scroll down to Scripting of Java applets
Step 5: Make sure the Enable radio button is checked
Step 6: Click OK to save your preference
Restart your browser and if it doesn't work try restarting system itself.
Hackers never learns but always wins!