I have an old Pentium IV 530J CPU that came from a machine with a dead D915 chipset.
Will that old CPU work on newer models of motherboard for LGA 775 without concern?
You need to check with the specific motherboard manufacturer for a list of motherboards supporting that particular processor.
You might want to check the Intel motherboards based on chipset 915 and 945 to see if any of those motherboards supports that processor:
But any other motherboard newer than those will not support that processor.