If she has complete dementia, you will likely have to establish a conservatorship. But depends on what you need to accomplish for her. Make a very careful search of her records and see if she named you on any joint tenancy bank accounts, or perhaps signed a DPOA but hid it " for a rainy day". or anything like that. If you need to sell real estate, you will probably need a conservatorship- see a local attorney who works in this area.
If your mother is not competent you will need to apply to the probate court to be appointed guardian. A person that is not competent cannot sign a power of attorney. They need to be able to understand their actions. If she is not able to understand a power of attorney then you will need to seek a guardianship.
You should speak with a probate or estate planning attorney to determine how to proceed.