You are misreading what the form says. I don't know exactly what you are looking at on Form 8332, but it does not say that you cannot claim other dependents. It says you cannot claim the "Credit for Other Dependents" for the dependent for whom you are not the custodial parent. The Credit for Other Dependents is a tax credit for a dependent who is 17 years old or older, or who is not your child.
Form 8332, or the lack of it, does not affect your ability to claim a dependent whom you are entitled to claim without a Form 8332.
