Unfortunately you cannot get your Grandmother's POA because of her dementia.
In order to care for her and make decisions on her behalf you would need to go to Nevada and obtain a guardianship.
It is recommended that you retain local counsel to assist you.
I have also attached a resource that describes the guardianship process in Nevada.
The only way to intervene on your grandmother's behalf at this time is through a formal court ordered guardianship. You should speak with a qualified Nevada attorney who can explain the procedures and help you gain control over your grandmother and her estate.
I agree with both prior posting. Unless a prior Power of Attorney was completed, it would likely not be valid at this time. You would have to file for a Guardianship, you may be able to qualify for a temporary because of medical issues, pending the hearing on to get a final Order. It may be difficult if you live outside the State of Nevada and do not have someone here who can assist. Consult with an attorney who handles guardianship cases quickly because the longer there is delay the more detriment that will come as it relates to decision making.
Generally speaking a power of attorney is a contract allowing someone to act on your behalf. A person who is not mentally capable of comprehending the terms of the contract cannot legally enter into the arrangement. From your description, your grandmother's dementia has reached the point of her being incompetent to sign a power of attorney. In order for you to take charge of her affairs, you will need to obtain a guardianship of her person and estate through the courts. You will be most successful if you contact a qualified attorney to assist you in this process.
As to the rent, she may still owe some rent if she signed a lease agreement. That will have to be negotiated with the landlord, but an attorney will be able to assist with that arrangement, as well. If it is a month-to-month arrangement, no rent would be owning if she has moved out and her personal property is no longer there.
The comment provided above is intended as general information and IS NOT LEGAL ADVICE. You should consult an attorney for advice regarding your individual situation. If your question concerns an Estate Planning matter governed by the laws of the State of Nevada, please contact my law firm for personalized service. www.probatebusters.com
If you believe your grandmother is in danger here in Nevada, contact Aging and Disability Services (I've included the link with this answer) and/or the Public Guardian for the county in which she resides.
I can see how you're approaching your question with the solution you think you need for your concern, but also reach out to the hospital social worker to find out what is going on and whether the public guardian and/or ADSD has already been contacted. If she is in Clark County, call 702-455-4332.
Best of luck and I hope things resolve well for your grandmother soon.