I'm new here so hope I'm posting a response in the right manner and am not offending someone by my words. My sister has been in the same situation as you. There are several things you can try.
Step One: Call the local Catholic Social Services in your area. They may be able to help you.
Step Two: Just pay as much as you can on the electric bill. Don't call them. Don't ask them what to do. Just pay a little bit and see what happens. In the meantime...
Step Three: Apply for welfare. When a family is on welfare and declared low income, the utility companies cannot shut of the utilities, especially if there are children in the home. (At least, this is what my sister discovered).
I hope this helps in some small way.
May God bless you and your family. May He keep you safe and warm, and provide for all your needs. May He provide the necessary funds to pay this bill. Lord have mercy! Lord have mercy! Lord have mercy!
In Christ, Athanasia