Starter solenoid PN

The jump start was not nice to something

That purple wire is back feeding the ignition switch and powering the dash so with it disconnected from the other wire, it would seem logical that the dash behaves normally

If I was curious, I'd pull the ECM relay and fuel pump relay and hook the battery up and see if anything changes while you're waiting on your new ones. 

Maybe you'll hear "the sounds of silence" 

Like I said, I have a thought or 2 but we'll see how your wiring checks go first

Going back in time, prior to the new starter relay and after the new key switch installed, this is something I tore into. In fact I had the alternator disconnected and COMPLETELY out of the boat. At that time, I started the engine and it kept running even without the alternator installed. I went to the safety kill switch and it had not effect. Now, at that time I wasn't paying attention to any of the dash  (Ignition and Engine Light) to see if those were lit up upon battery connection. Again, the only thing that would kill this beast was to pull the distributor wire. And, with alternator removed, it still made that (1) second buzz sound when battery was connected. To clarify, this was AFTER new ignition key switch installed and BEFORE start relay replaced. I'm still going to verify my wiring per your schematic, however my removal of the alternator may have covered your "green wire" theory.

Short answer.......Yes

But what I think you should do, that'll take maybe 5 minutes is to unhook the green excitation wire from the back of your alternator, hook up the battery and see if the pumps prime or you hear nothing happening.

No noise or priming would mean that your alternator kinda "took a hit" on the jump start.

After the jump start, with the engine running it would make your engine run with the key off and with the kill switch removed and you'd have to pull the coil wire to kill it because the alternator is backfeeding the ignition system.  Sound familiar?.

With the battery disconnected like you have it now,  when you hook up the battery, with the green wire hooked up it would be backfeeding battery voltage from the alternator to the ignition system purple wire and making the pumps prime for a second or 2 like when you turn the key to the Run position

That would mean an internal diode failed and even without the alternator running it feeds voltage into the excitation wire and that wire is hooked to the purple ignition wire

With the wiring verified to be right, then you should be able to turn the key, have the boat start and be able to turn it off with the key, but your alternator wouldn't do any charging..

I hope that's your problem (and that would mean you didn't screw up any wiring) 

But you'll need a new or rebuilt alternator.

I've had this happen with a couple of alternators over the years and it's kinda spooky when the engine is still running and the key is removed and in your hand 

Here's another diagram that shows more than just the solenoid. It may be helpful

It seems like your original "it won't turn off "issue happened way back when you got the jump start though, before replacing anything and having a chance to wire things right or wrong.

After hearing back on the wiring checks, I nay have something for you to do, but we'll wait on that for now 

PS.... I'll predict that you have all the wires hooked up right

The 2 relays are exactly alike and you need 2 good ones to make the engine run.

Swapping one for the other isn't gonna tell you much and if one is bad, the engine won't run

You can get the relays at most any auto parts store. You ask for a Standard Motor Products RY 241 relay or an Echlin AR 174 relay or anything that cross references to those numbers. The PCM part number is R130011A but the others work just fine

It's always a good thing to have a couple good spares around for "troubleshooting" or to make your engine run again It could also be one of your fuel pumps running when it's not supposed to. 

One of the relays or pumps has a good chance of being the noise you hear

I'm running the GT40 Pro Boss 351W Fuel Injected.

My Ignition light stays on the moment I connect +battery with the breaker in AND out. Somehow I'm getting 12v to the Purple and Lavender wire and not the Red (B) wire. Something is backwards.

Should I be hearing a buzz at the rear of the engine when I connect the +battery? I'd expect to hear that only after I hit the ignition breaker and turn key to first position.

FWIW I've not tried to start the engine since the new starter relay was installed....

Thank you for the interest.

Last Fall I went to launch and needed a jump to get the boat started. I realized that I left the Ignition Breaker "ON". From there, it was a normal day until I went to turn the key to "OFF" and the engine kept on running. The Safety Switch next to Throttle was ineffective in killing the engine, so I went to the distributor wire and that shut it down. Since then, I replaced the key switch (Red wire to B, Purple wire AND Lavender wire to I, and Yellow/Red to S) and  replaced the 20amp Ignition Breaker.

This did not fix the issue.

I did notice that every time I connected the battery during this process, I heard a buzz at the rear of the engine.

This brought me back there to replace the Starter Relay. Upon that replaced, I still hear the buzz as I connect the battery and now the Ignition light is on next to the Ignition Breaker (whether it is In or Out) and the Engine Warning Light is on. I took the key ignition switch completely out of the system and these symptoms continue. With that, at the wires that go to the key ignition switch am getting 12V at the Purple and Lavender wires and 0V at the Red wire. All of these symptoms occur with the key position in off and key out of the switch.

However, the Safety Switch is now operable as the lights go off when clip is removed.

I'm chasing a ghost here. Could be I added/missed a wire when I swapped the key switch? Could be I installed the Starter Relay incorrectly ? Thoughts? Suggestion? I thank you all in advance.

Mark

With that said, I KNOW I did NOT disconnect this beast, coming from the main harness, starboard side, and the corrosion and dirt on the press fit would indicate it's been sitting around. Test port for the Rotunda? Haven't pulled up the diag. yet.

Here's a diagram I drew or scribbled or whatever  

The "s" and "i" are labeled on the solenoid itself.

Any wires where I didn't mention wire sizes are small like 14 or 16 gauge.

It's different than the wiring on a mid 70's 351W for example