1. When did you buy the computer?
2. You say that you noticed the 'hang up' problem on the first day - what exactly is this problem, and under what circumstances does it happen?
3. When did the engineers make their first visit, and who were they from?
4. What's all this about a 28 day refund policy - where did that information come from?
5. What do you mean by "computer nowadays has a self repairing function"?
6. What make of PC are we dealing with here?
7. Have you at any point written to PC World about the problem(s), and if so, did you get any response?
Protecting your personal data is your responsibility, and I think you must give up any thoughts of compensation for loss of that. If you have critical information and/or images on your machine it is only commonsense to back up to CDs or some other external media, PC World are not liable to you for loss of data.
You're protected against a faulty computer by consumer legislation, but in order to be able to advise you specifically we need answers to the questions I've asked.