Since I don't use Vista or have a sidebar this is all a search exercise for me here. Here is one thing I have found;
This behavior is observed if the XML registration is missing in the system. To fix the problem, use the following steps:

* Close Windows Sidebar. To do so, right-click on the Sidebar icon in the Notification area and click Exit
* Open an elevated Command Prompt window. To do so, click Start, click All Programs, click Accessories, right-click Command Prompt, and then click Run as administrator.
* In the Command Prompt window, type the following and press ENTER:

regsvr32 msxml3.dll

Similarly, run these commands:

regsvr32 scrrun.dll

regsvr32 jscript.dll

If the registration was successful, you'll see the message DllRegisterServer in <filename> succeeded for each command executed. Open Windows Sidebar (sidebar.exe) and check if the problem is resolved.

Also sounds as if either your Java is to blame in IE7...maybe disabled or a "broken file" in the browser cache is stopping you from seeing iGoogle page...try this;
  1. From the Tools menu, select Internet Options... .
  2. Choose the General tab.
  3. Under Browsing history, click Delete... .
  4. Next to "Temporary Internet Files", click Delete files... .
  5. Click Close, and then click OK to exit.
Then use File, Exit on the upper left to close IE7. Then open it up and see if this helps.
All of these problems you are having point probably to a downloadable "gadget" in the browser or sidebar. These all are extra add-ons and do develop trouble from time to time. Obviously the problem lies somewhere in IE7 since you say that Firefox works fine.