These situations are always very difficult. I am sorry to hear about even more that you are going through. The reason I asked the question is that Conservatorships should be the last option. The Conservatorships will remove all your father's legal rights and his Conservator will take over full control over him. The Conservator has the right to decide where he lives, where he gets medical care and is in full control of his finances.
With all that said, the initial petition is done by you filing to have him adjudicated incompetent. Since the initial proceeding is you against him the attorney must be hired and paid by you, not him.
You have several options other than hiring a private attorney.
You could check with the social worker to see if adult protective services in his area will file the conservatorship petition and request that you be appointed his conservator since you do not have the funds to hire an attorney. http://www.cdss.ca.gov/agedblinddisabled/PG1298.htm
You can take steps to file this on your own however, it is very hard to do so far away. There is a great self help website for California here if you want to try on your own. http://www.courts.ca.gov/1302.htm
Finally, you could also check to see if you would qualify for California legal aid to help you file the conservatorship petition. Here is a link to California legal aid. http://lawhelpca.org/issues/seniors
I cannot provide you with legal advise. I have provided you with information about the law related to your question. My answer, and any information that you find online, should not take the place of having a consultation with a lawyer in your area to advise you regarding your specific issues.
Please show your appreciation for my candid, accurate information by clicking VERY INFORMATIVE, OR the OR and positive feedback. You should only rate me if you are satisfied with the information I provided you. If you cannot rate me GREAT please do not rate. Give me a chance to make it right by clicking REPLY TO EXPERT.
I appreciate your question and repeat customers. You can request me by beginning your question with "Dear XXXXX..."