In order to answer you quickly, I need to type in English.
First, you need to know how much you are going to claim, if the amount is over HK$50,000, then, the small claim tribunal will not accept your claim. If you said several computers, I guess the amount to be claimed will be less than the limit.
The application is easy. Go to website of info.gov.hk and search under the cateogry of judiciary. You will find more info such as application fee, forms to be filled, addres of small claim tribunal etc. You need to pay the application fee only and there is nothing about court fee. The spirit of small claim tribunal is to avoid the huge amount of legal fee and time for people to settle the claim. However, please bear in mind that under the operation of the small claim tribunal, you have to prove that the moving company owes you money, therefore, you shall have evidencing documents such as contract, demand letter, photos of the damaged computers to support your claim.
I just think you shall consider to go to consumer counsel instead of small claim tribunal because there is no established claim at this moment. Anyhow, if you need further assistance, please give me a call.