Looks like someone has some wires swapped around in some connectors. Do the slings fire at all with any other switch hits?
Hopefully someone can send you a picture of the J2 and J5 connectors and wire colors on the solenoid driver board (SDB). But it looks like someone has the left sling (SDB: J2-4) wired to the first 'E' target (SDB: J2-12). Then the right sling (SDB: J5-11) wired to the 'R' target (SDB: J5-14).
The question is what are the sling coils wired to??? If they're simply swapped around, do the rollovers above the METEOR targets or any of the lit inlanes fire the slings? If so, then you've got those coil wires swapped around.
At this point you could just swap J2-4 and J2-12 as well as J5-11 and J5-14. It won't hurt anything. Just release the pin lock and swap the connectors and wires in the housings.