Have you actually tried swapping the polarity anywhere?? Maybe even on the Spyder end?
More than one member here has been caught out by the Spyder's wiring being the reverse of what it's meant to be &/or what the documentation says it should be, and swapping the polarity shouldn't hurt the LED's either individually or as a kit; but the bottom line is that if you've got one LED or a string of LED's connected the wrong way around, they just won't work, even if the filament globes you just took out of that circuit all worked a moment before.
So again, I'd suggest you check the polarity of your LED's - heck, if you're concerned, just connect the + & - wires of the kit &/or each individual LED in turn to a suitably fused lead direct from the battery; and if they don't work one way, try them the other way! At the very least, you'll establish that the LED's in the kit DO actually work... or not! And along the way, you juuuust might find out why they don't work the way you've currently got them installed.
It shouldn't take long, and it shouldn't hurt anything - LED's connected with their polarity the wrong way around don't blow, they just don't work, exactly what you've told us they're doing at the moment. And even if they still don't work, you will have positively exclude polarity as being an issue.