You don't have to go to court for a power of attorney. All you need to do is to have your father sign a power of attorney before a notary and two witnesses. Although he has dementia, he can sign a power of attorney, so long as he does so while in a lucid state. Once it is signed, it is good for the rest of his life (unless he wants a shorter term), even if his mental state deteriorates later. You should get him to sign one before his state deteriorates.
If he wants to make a will or a living will, he should also do that while he is still more lucid than not.
I can help you with the power of attorney, if you like. I can also notarize the document, if your father is in or near the New Orleans area.