“Can back child support be requested for a time period wherein the custodial parent moved away without notifying the noncustodial parent, and that parent had no idea where to even send child support payments? In this case, there was no child support order through the court. There was only an informal child support agreement.”
Under the circumstances you describe where there is no actual court order for child support, the custodial parent will not be able to get an order for support retroactive before s/he files. Of course if that custodial parent has been receiving public assistance, the governement can go after welfare reimbursements against the non-custodial parent for payments made up to 3 years prior to their catching up with that other biological parent.