Is there a free, nominal County or other governmental agency to obtain a POA and guardian for an elderly person?

You might also contact the New Jersey State Bar Association; look for the Estate Planning and/or Elder Law practice area groups. These are subspecialities in the field that would address POAs and Guardianships.

Be prepared to provide documentation on your mother's low income status so they can justify providing services pro bono or at low cost.

Let me give you an example - I typed "little rock elder guardianship pro bono" in my search box and found this:

Volunteer Organization of Center for Arkansas Legal Services
www.arlegalservices.org/vocals
Center for Arkansas Legal Services
What if I'm already a member of Arkansas Volunteer Lawyers for the Elderly? ... a wide range of civil legal matters such as guardianships, bankruptcy, divorce, housing ... Pro Bono law students at the University of Arkansas at Little Rock Bowen ...

Have you googled with your location and checked with Area Agency on Aging?