How do I to get help for my elderly neighbor with dementia who has no family near?

DHR may not do anything because you haven't said she has dementia. Also, have you called your county's Department of Health and Human Services and spoken to social services? Report her to Adult Protective Services. You can call animal control regarding the cats and that may get her on someone's radar. But if she's in her right mind then she can make her own decisions about continuing to live the way she does. Or, you can have a conversation with her about what will happen if she doesn't voluntarily request help from them (when it gets bad enough the county will take guardianship of her and place her in a facility -- which is actually what she needs). Is she aware that she can request in-home services? You are a wonderful person for having such concern for her. I hope she will allow you to help her.

Well you paint a grim picture. How does she think she’s doing?
You can contact your local Area Agency on Aging and report her condition and/or the local Adult Protective Services. Even the local animal protection services might take an interest.
Hopefully she won’t resent the interference.
Here is a link to try.

https://www.macoa.org/

I would call the local area agency on aging and tell them what the situation is, they will report to the proper authorities that can get her help.

God bless you for helping her get the care she needs. I wish everyone had a neighbor that cared and paid attention.