(Posted in 2 parts - it's a long answer!):
Some people don't like cookies on their system but they're harmless so no worries there. (The only worry that most people have about cookies is that they usually name the site which created them. So, if the local vicar returns his loaned computer to the the church council, he might not want a cookie named 'hornysexbabes.com' left on the PC!!).
People can do nasty things to your computer via Java Script but, as long as you've got up-to-date anti-virus and firewall programs, there's no need to be frightened of it!
Assuming that you're running Internet Explorer - you poor, sad thing -here's how to check that you've got the required setttings:
Go to 'Tools' then 'Internet Options'.
Select 'Security' and check that the 'Internet' zone is highlighted.
Select 'Custom' security settings.
Look under 'Cookies'. You should find two entries here (for different types of cookies). Check that there's a dot in the circle next to 'Enabled' for both types.
Look under 'Microsoft VM' - 'Java Permissions'. Check that 'High Safety' is selected. (If you still can't get into the website you want you might have to return here and try a lower safety level).
Look under 'Scripting' and check that 'Scripting of Java Applets' is enabled.
Click 'Apply' then 'OK'