Oohhh. Connectors broken off......there's a monkey wrench in the works. OK.....you should be able to run the engine without the gauges.
Are you saying you "lost" the other side of the purple wire that you cut?
You shouldn't need to bypass them, in the true sense of the word. You should still be able to operate the boat with them still hooked up. They may not tell you anything useful., but they shouldn't keep the engine from running. (Do tape off those that go to the broken gauge connections.)
Do you get anything that resembles electrical power? At this point, I suggest you double-check all your fuses. You may have popped one that's not obvious.
Roger