In the IIS config, is default.aspx set to have a higher priority than index.html? If it worked previously, probably it is, but you should still check the default settings for the new domain.
As long as they did a copy-paste type move of the files, it should be as easy as adding the domain name in IIS and pointing it to the directory, then adding an appropriate portal alias record in the database.
Check the web.config file to make sure the database connection string is set properly, as well as the "keys" for everything. If when they moved the dnn install they actually did a fresh installation of dnn, then you're pretty well out of luck unless you have a copy of the old web.config to copy over the keys for everything.
You may be stuck with just wiping everything out, dnn installation and the database, and starting over from scratch with a fresh install. One thing I do quite often is to create a portal template on the dev site and use it as the template while installing a new portal on the live site, it generally copies all content over except the blog, and image links in the Html module end up broken. But, it saves time in regards to the hassles of copy and paste dnn installations.
Also, you really didn't need to move the dnn install to a new directory. Often, when transitioning a website over to a dnn site, I just add a new directory for the dnn installation, but leave the current site and domain settings pointing to the root. You can access your dnn site being developed by domainname.com/dnn/default.aspx. Then when you are ready with the dnn site to go live, all you need to do is change the domain name settings to point to the dev directory as the domain root and update the portal alias in the database. Purchasing a second domain for a dev site and then trying to move the files to a new directory is really very unnecessary and only creates a situation where you can end up with the site broken as it is now.
If you need a dev site where there is no chance of anyone ever stumbling upon it, I'd install Visual Web Developer Express and running it on your personal computer, then when you are ready for the live site, again, you export a portal template and use it to create the new portal on the live site with only very minor edits to clean things up.