BSEIndia works fine on my system any time. The cross sign in your screenshot means that either Java is disabled on your system or you are using a non existent java virtual machine ..
As I cant find any pc near me which is running IE6, you'll have to search for the settings yourself .. Try Tools > Internet Options . Click on Advanced tab .. Java should be there .. Check the settings ..
Also, check the network setting in Java control panel .. This should be in Control Panel > Java ... Or Start > Run > javacpl.cpl {Press Enter} .. If you are using a direct connection to internet, specify the same in javacpl ..