How are your repair skills?

Do you have a multimeter? Do you have a logic probe? A schematic?

Do you know how to use them? Can you look at a datasheet for an IC, and understand how it works?

There's something else that's causing the 374 to engage the transistor, most likely.

Using the logic probe, you could check the state of the IC, see if the leg connected to your predriver is in the wrong state, look at the input leg of the 374 and verify whether or not the leg is in the correct state, and trace it back through the board. Or, something from that solenoid is somehow backfeeding voltage back to the driver board. That's a possibility, too. You could check the transistor with the logic probe, with the playfield solenoid connector unplugged, and then with it plugged in.. or, check the connector for voltage while it's unplugged from the driver board.

It'd be tedious.. you'd learn something.. but a lot of people just prefer to send the board out.

There's no harm in making either decision - just comes down to comfort level, amount of time, having the correct tools, etc.