Can I become POA for my dad who's now too ill to make his own decisions or is guardianship the only option?

Are you able to communicate rationally with him? If so, he may not actually be mentally incompetent for purposes of signing a will or choosing you as POA (medical & financial). If he can say, yes I want my daughter to make all decisions for me, As aAKdaughter said, he can just make a mark for his signature. By all means, start with the social worker at the hospital where he is staying. BTW, this site has some excellent information regarding wills, POA, guardian, & conservatorship. Try looking that up also.

It is my understanding that he doesn't need to be physically able to sign his name (he can make some kind of mark that is witnessed by a notary), but he does have to be mentally competent to appoint anyone as his POA. If he is not competent, you may need to contact an attorney to be appointed as his guardian. If he is currently in a health care facility like a hospital or skilled nursing facility, ask to speak to the social worker. He or she probably has experience in these situations and can get you started in the right direction.