Yes with no pin the brakes should be locked if there is power to them. They may be worn out also. Could also be the brake solenoids are also bad.
You can buy replacement pins, but they must be exact replacements and pull easily. The 7" replacement is about right. That is the size that I purchased for my dolly when I converted to electric brakes. The length of the wire can be increased if necessary.
If you have a good battery on the trailer you do not need a stand alone battery. I put the battery pack on my dolly as the dolly does not have a battery.
It sounds to me by your post that you have an 89 trailer and the brake system should be gone through thoroughly and be repaired where needed. JMO