Windows – Why does Internet Explorer repeatedly prompt to reinstall Silverlight

Try editing the registry. Make sure to open the 64-bit registry editor. (you have to close the 32-bit one first).

Go to the registry key HKEY_LOCAL_MACHINE\SOFTWARE\Classes\http\shell\open\command and set the (Default) value to the path (from the 64-bit point of view) of 32-bit IE, which might be "C:\Program Files(x86)\Internet Explorer\IEXPLORE.EXE" -nohome (the "-nohome" is a commandline option which my copy of IE8 adds to this value)

You might want to do the same for the classes https and even htmlfile if you want to double-click HTML files and open them in 32-bit IE.

All this won't help if a 64-bit application executes iexplore.exe directly instead of launching a URL. (in fact I haven't tested my suggestion at all because I don't have 64-bit Windows. Nevertheless it might work)

Internet Explorer uses your Windows proxy settings when connecting to the internet. I'm not sure about Chrome, but Firefox can use its own settings.

So maybe some of the malware changed your proxy settings to redirect you to some specific website. If the browsers have different settings, then that might explain why one browser can connect but another cannot.