You cannot generate a pdf with Acrobat. Reader is just that for reading pdfs.
If you only have Reader, you can not create a PDF. You would need Acrobat.
If you are "saving" as a PDF from Word, you are using the Microsoft PDF utility rather than Adobe's. You'll want to ask Microsoft support.
Could you provide me with some guidance on what kinds of things I should try and troubleshoot?
Contact the support of Microsoft.
Adobe Acrobat is a good choice.