What board -- factory or aftermarket?
For J1 -- older machines used 8 pin connectors. Aftermarket boards use 9 pin connectors and the 9th pin is unused when used in older machines.
If this is the case - to avoid confusion such as yours, I recommend always replacing J1 thru J3 with new connectors and contacts. New plug at J1 would be a 9 pin plug with the 9th pin unused.

All pins should line up. The bottom connector is for the backbox, that's pretty obvious unless someone split the 20 pin connector. The cabinet connector goes on the upper right and the playfield connector goes on the upper left. Can you post a pic?

Pretty sure they have pics/diagram for wiring up a rectifier board for a Classic Stern pinball on Pinwiki.

Just as mentioned on post #2.
That is an aftermarket rectifier board which includes the extra pin on J1.
Either use the 8 pin plug as is and leave the 9th pin exposed as shown in first photo or replace the 8 pin plug with a 9 pin plug and don't use the 9th pin.

By the way - that is an awesome quality rectifier board
Also, that board is sold by manufacturer with a complete connector set including a 9 pin plug for use at J1.

And don't forget to install the finger guard on when done - lawyers love seeing exposed 120VAC lines!

Also also - might want to look at the connectors anyway. At least one of the pins on the 24 appears to have been running hot and should be repinned.

For that - I'd start with the 5V regulator circuit on the solenoid driver board.
Start here:
http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#Solenoid_Driver.2FRegulator_Test_Point_Values
and here:
http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#Solenoid_Driver_Upgrades

Note - the stern board is a knockoff of the bally board.

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