Zoe is a very wise woman (because she agrees with me! :D). When we are panicked about something that is not immediately threatening to our physical well-being, it is generally because we’re viewing a situation as overwhelming and infinite. Very few situations are. When we are panicked, we need to look at the actual situation, and see what it consists of. No matter how big a problem may be, it has limits. Once you’ve established those limits, you can stop panicking and actually start dealing with the situation.
In this case, you’ve got some fairly concrete things to deal with, and they are certainly not infinite. You have to bear in mind that it is in your new company’s best interest for you to succeed, as well as your own. It costs them money to hire you, it costs them money to employ you, it costs them money to fire you and to hire someone else. They would far rather keep you than to let you go and hire someone else.
If you have some lead time before your starting date, call them and ask them exactly what platforms you will be working on. Explain that, in your spare time, you want to be getting a head start on your new job. This will certainly do you no harm in their eyes, and will enable you to know where to focus your learning efforts. Then, since I imagine your finances are tight, bear in mind that the internet is your friend. There’s huge amounts of information on technical systems available without spending a penny.
Java syntax, if I recall correctly, is virtually identical to C syntax, so brush up on your programming in general. I’ve been programming professionally since 1977, and my experience is that programming is programming is programming. The biggest problem is learning the quirks of your particular environment that are going to force you to get creative in order to do what you want to do (and each environment has those quirks).
No one is expecting you to come in as an expert. Even if your resume precisely matched their requirements (and you know that never happens), you don’t know their business environment. They’re going to be watching for a couple of things. First and most important, are you trying hard? Are you making the effort? Second, do you have the skills they need? That doesn’t mean that you have to know the environment, but rather that you demonstrate an ability to learn and understand how to use that environment. If you were a good programmer before, the chances are you’ll be a good programmer again, that you’ll be able to pick up what you need.
Again, let me reemphasize: they don’t want you to fail. It’s in their best interest to help you succeed. Between that and your own abilities and efforts, you should be fine.
Remember, make a list of the problems/actions required. No matter how long the list is, it won’t go on forever. Once you have it, you know the limits of your problem and you can get started dealing with it. This is true for any anxiety situation, not just yours.