to a url. It doesn't matter where your site is, but it has to be on a unique address, otherwise there's nothing point to.
You can point a domain to a static IP address, but then you must have an index.htm file at that address, otherwise browsers won't have anything to locate and download. Normally your new host would tell you to FTP the files into the server using your domain name, but as you don't have any name hosted on that server you have nothing to FTP to.
If your new host offers cheap domain name registration you could register any name, have it hosted on your server space, and then point your old name to it - that would be very straightforward, but to be honest it doesn't seem worth it. Your old host should retag your domain name as soon as you make the request - it doesn't take more than a day or so normally. Then you'll have to wait up to 24 hours for the new location to propagate on DNS databases around the world. If your old host company is dragging its heels over this why don't you badger them on the phone?