What is the ruling concerning the new profits generated from an investment deposit; are they all Haram?

The ruling on new profits is the same as the ruling on old profits. Its ruling depends on the bank's activity and how it invests funds. If it invests in Sharia-compliant areas, there is no harm in benefiting from the profits. However, if its activity is forbidden, then the amount of that forbidden activity is prohibited. One should act according to the predominant assumption in this regard.