Push Starter Button Not Enabling The Starter Motor To Engage. Advice Please

[Lord Hellcat]

So the Hellcat has been sitting idle pretty much since the end of September when I had a clicking noise coming from the supercharger when you switched off.
We pulled the supercharger and sent the snout to Jon Bond. The pins and bushes were worn and replaced.
I asked them to check the operation of the Litens 2.85 and it was given a clean bill of health.
Back in February we refitted the supercharger and much to my distress the clicking noise was still present.
So I ordered a new Litens pulley from HHP and Liam my mechanic finally got around to fitting it today.
Thankfully the noise has gone.
Whilst laid up the battery died and we fitted a new battery.
However when you cycle the engine to run and push the start button it will not crank the starter motor
The Hellcat does not have an immobiliser fitted, we pulled the starter motor relay and switched it with another relay, still no good.
So Liam then tried a link wire where you cycle the engine to run, hold your foot on the brake and then use the link wire in the fuse box to crank the starter and it fires right up. You only hold the link wire in the fuse box for as long as it takes the engine to fire.
Any thoughts on what might have failed please

 

[covidcommander]

New push button switch

 

[Unholy707]

So the Hellcat has been sitting idle pretty much since the end of September when I had a clicking noise coming from the supercharger when you switched off.
We pulled the supercharger and sent the snout to Jon Bond. The pins and bushes were worn and replaced.
I asked them to check the operation of the Litens 2.85 and it was given a clean bill of health.
Back in February we refitted the supercharger and much to my distress the clicking noise was still present.
So I ordered a new Litens pulley from HHP and Liam my mechanic finally got around to fitting it today.
Thankfully the noise has gone.
Whilst laid up the battery died and we fitted a new battery.
However when you cycle the engine to run and push the start button it will not crank the starter motor
The Hellcat does not have an immobiliser fitted, we pulled the starter motor relay and switched it with another relay, still no good.
So Liam then tried a link wire where you cycle the engine to run, hold your foot on the brake and then use the link wire in the fuse box to crank the starter and it fires right up. You only hold the link wire in the fuse box for as long as it takes the engine to fire.
Any thoughts on what might have failed please

Can you shut the car off via the button after doing this?

 

[BULL]

Subbed