I am a website developer and have often walked into your situation. The original developer is either unwilling or unable to continue support and the customer wants me to access the website for changes. Usually the developer arranges purchase of the domain name, pays for registration and pays the web hosting fees to another service. It is a VERY common situation you find yourself in. If your site is being hosted, you have two problems; gaining control of the ownership of the domain name, and gaining control of the hosting site. Your situation is so common, neither the registrar or the host wishes to expend any energy to help you. Here is my free advice:
Check your contract with the developer to see if you have any contractual leverage with the developer to relinquish control. Did the developer state he is to maintain control of the site? did you agree to pay for the services through the developer? Is there a termination agreement? Did the developer make any promises concerning service or support? Was there a time reference to the developer's work? Typically the developer has no right of ownership over your domain name but may have legal control of his work. A web host is more likely to provide you with the account information if you can prove you own the domain name. Either send a registered letter yourself or have your lawyer send a letter to the developer indicating that the developer's obligations have not been met and if the developer is not forth coming you will pursue damages. In my business, I provide the customer with all account IDs, passwords, copies of the transactions to the services and a CD with all code on the customer site. I state in my agreement that if any of the information is used without my permission, there will be no further contact, support or service from me. Most of my users value my service and abide by the understanding.
If the developer cannot be shaken and you don't wish to sue the developer in small claims court you have a few options left. If your domain name is based on a business name, trademark, or any other defendable entity, write the registrar indicating who you are and your situation on a company letterhead. The registrar and web host will usually try contacting the developer using the email address provided by the developer when the services were purchased. If the developer does not respond, and If the services are satisfied you are who you say, they will require you to jump through their hoops, possibly requiring you to FAX them something from the phone number listed on your site or providing a business license or some indication they can use to defend their actions if the developer won't relinquish control. Pesky persistence will usually pay off.
Otherwise, wait for the domain name to expire, purchase it again yourself, and purchase a host site. Hopefully you have copies of the code on the site. If you do not, again, the developer did not meet his obligation with you. If the hosting service expires, they typically delete the webspace within 30 days and you have damages that could be collected from the developer as you do not posess what you transacted from the developer. Good luck.