I'd be very surprised if Java isn't already enabled in your browser. To check, in Internet Explorer, go to Tools > Internet Options > Advanced, and make sure that there's a tick alongside 'Use JRE . . .".
If you're using Firefox, go to Tools > Options > Content and ensure that there are ticks alongside the two Java references.
The problem is far more likely to be related to the Flash Player plug-in. It has a nasty habit of 'disappearing' from PCs. (Your system will tell you that it's there. Downloading it again doesn't work because your PC thinks it's already installed).
The trick is to go to 'Add/Remove Programs' and completely remove 'Adobe Flash Player Plug-in'. Then re-download the player. Your PC will then complete the installation properly (rather than simply leaving the existing, non-functioning plug-in installed).
Chris