Hilary, thank you for your help. I'm going to attach the file, but the data sources are all behind password-protected SharePoint site, so none of the fields will actually work. I'll also attach a screenshot showing what should happen.
The error that I'm getting is once that it is published to a forms library, a message says that it will need InfoPath Filler to complete the form because the "data connections contain parameterized queries." I thought this was because some of the fields depend upon other fields, but even when I adjusted to form to only retrieve one piece of data from a SharePoint list, the warnings were still the same. When I removed all Data Connections, I no longer received the error messages.
The warning at publication says, "The form template has been published to the server but it can only be opened in the InfoPath Filler because it contains features that are not compatible with Web browsers. To fix this problem, close this dialog and review the errors in the Design Checker task pane." The Design Checker says that the issue is with all 3 data connections: Team Contacts, DocumentDetails, and ProductDetails.
The SharePoint lists are all on a SharePoint site that my users have access to read.