No visible firing pin mark on the primer is certainly an indication of a broken firing pin. Assuming you chambered the correct caliber ammo, of course. What caliber is the rifle?
Another possiblity is that dried oil and lubricant has gummed up the firing pin path, and preventing it from moving.
Stripping the Remington 740 receiver is fairly easy. You push out the two receiver pins securing the trigger guard assembly. Now you can access the back of the bolt/firing pin to check for free movement.
John