I do not know what country you are in, however, in the U.S. they would be required to refund your money. Contact them and try and get a refund. You should be trying everything you can do to give them opportunity to make this matter right. Be kind and polite when dealing with them.
What to do if this does not work?
I cannot speak to what is required in your country, however, I will discuss what to do in the U.S.
If GoDaddy does not return your payment, they would have to prove that you obtained services through fraudulent means in order to have a defense or that you were unreasonable in your demands. They would also have to prove that they acted reasonably and established an agreement with you to refund your money.
Their responsibility to you is to appropriately provide services and to have processes and/or procedures to prevent disappointment. They are then responsible to make right any harm when the company has acted in error. Failing to do this would be simple theft.
Given that, and assuming that they have not refunded your payment, you can file a small claims law suit. These can be filed by you for a small fee and do not require a lawyer. I always recommend talking to a lawyer prior to filing. There are plenty of lawyers that will help you with free advice and give you a strategy for court. Small claims court can not only award your payment, but punitive payments when companies fail to respond appropriately. If you make a claim including the request for punitive charges and if GoDaddy does not show up, you will get a default judgement.
This can be fun! I canceled my cable services due to the horrible cable company that had the monopoly in my area. The fact of the matter was their services was poor and not worth the money charged. I took 5 consecutive Fridays off from work in order to return their cable box. I was a consultant at the time and taking time off cost significant money in earnings. The Saturday after the 5th Friday they did not show up, I was served with a law suit for the theft of their equipment. As a company, I had a lawyer and called him quickly. I filed a counter suit at 8:30 Monday morning.
Long story short, the Judge yelled at the cable company for quite a while. He made them face me and apologize. When they mumbled, he yelled again and made them speak into the microphone. It is now in the court record. He dismissed their suit and awarded the earnings I lost the 5 days waiting, plus court costs and loss of earnings going to court, plus punitive payment required to be paid before leaving court. They had to write a check in front of the judge and enter it as a matter of record with the court secretary before they could leave. This meant that someone have to bring a check from the office (which was not close) and they had to wait. Lawyers were made to sit in front of the judge waiting. Great fun!!