You will require creating domain accounts and modifying the accounts that SharePoint runs as. Typically best practice is not to run a web application of any sort on the domain controller as you are opening a security hole.
Now, in your case, I would backup my content databases, create two domain accounts (one for core service account and one for search). As an administrator, reinstall the instance of SharePoint, using the two domain accounts per the deployment guide that Microsoft has released. From there, set things up as you previously had, then reattach your content databases.
That should get you back up and running.