I'm filing conservatorship for my dad in California. My dad is a California resident. I need to sell his home in Illinois. I was told that because the conservatorship in California does not have jurisdiction in Illinois, I can't proceed to sell his home in Illinois.

Do I have to file for guardianship in Illinois also? If not, what do I need to do?

I'm really not sure - I suggest you try to speak with an attorney to determine what is required to have legal powers over assets in Illinois.