Bring proof of income for each household adult, the Social Security card for each household member, a copy of your disconnect notice and the written statement from FIA of what it will or won't pay. And many agencies won't help with deposits. No agency can stop a disconnect that has been scheduled for the same day. Act early on your dilemma. Plan to pay at least some part of your bill.
Agencies have limited money, especially the churches.
In many cases, they can only offer one-time help for emergencies. Help with heat always goes directly to the utility company, not you. It does you no good to place your utility bill in your child's name. When you seek utility assistance, agencies will need to see the bill in your name. If you seek help from more than one agency, always bring the paperwork from the other agencies, too.