If you've tested components from the transistor to sling and all is OK then it must be back to the board. There will be a "buffer" chip between main logic chip and transistor.. its there to protect the main chip. Im not familiar with sys11 games but preceding SS games always have this feature in place ( normally a 7407, 5407 or similar). That's where I would be looking next... it may well have more than one transistor fed by its gates.
Dig out those schematics!