My grandmother's POA was my mother, who passed at the beginning of January and no other POA was created. My grandmother's dementia recently has gotten worse in the past week, to the point where she is almost non-responsive. What do I need to do to become her POA so we can pay for her assisted living and any medical care?
For medical, most states do have a mechanism in place such that next-of-kin can make or authorize medical decisions, if a person is incapacitated and has no available durable power of attorney for healthcare.
You will probably need an attorney, but you can learn a lot about your options by first contacting caregiver resources, such as your local area agency on aging, Family Caregiver Alliance (look up their website), and also any local non-profits that serve older adults and families. The assisted-living facility staff may also be able to help answer your question, they have probably encountered this situation before. There may also be a social worker available at the doctor's office.
Agree with @helpnga that if her mental status has declined fairly suddenly, she should be checked for causes of delirium, which include UTI, other infections, and much more.
Good luck.