Hi there,
Thank you for reaching out and sorry about the trouble.
As per your description, you are using the Document Cloud account to combine PDF online. Please ensure that once you add the files to combine, enter a new name for the file in the box provided at top right corner in that window. Please check the screenshot below:

The combine button highlights only when you add a name for the file that will create after combining all the files.
For more information on Combining documents into PDF or Document Cloud, please refer to the following help documents:
Combine documents into PDF: https://helpx.adobe.com/document-cloud/help/combine-files-pdf.html
Document Cloud: https://helpx.adobe.com/document-cloud/faq.html
Hope the information helps.
Let us know if you need any help or experience any issue.
Thanks,
Meenakshi