I got it working. Here's what it took:
* Import all of the tables Ivan suggested from my old database to my new one.
* Changes the ApplicationID column in telerik_users and telerik_roles to match the new ID in telerik_Applications (I suppose I could have changed the master applicationID to match the old database alternatively).
* Copying and pasting rows in SQL Management Studio leaves Boolean fields null. This was a problem in the telerik_users table.
* After this, I could log in. Now I encountered the next problem: The role feature is disabled in web.config by default. This thread explains how to enable it
Thanks, Louise for the article. I tried following it first.
Unfortunately, when I browsed to cmsstartup.aspx, it redirected me to the login page. I have some theories as to why but I didn't troubleshoot it.
Thanks for all your help. I'm back in business.