gsx750r93

So i just bought a sc400 the other day with a bad starter for cheap. On a side not it has been sitting for a year not being ran.
While replacing the starter I began to notice how brittle all the connectors where.

The Coolant temp sensor broke into pieces while taking it apart also. It is not connected anymore and is completely toast.

After first start up-
It ran but knocked really bad..
Let it idle for a while while the knocking slightly went away. I am guessing the knocking was from it not being started for a while. After idleing for a while it died and that was it. It was getting late and with many tries turning it over it nothing and called it a night.

Next day second start up-
Started right up with a faint knock.
Finally no more knock and it ran absolutely perfect so I decided to take it for a drive.
After about 5 mins of driving it died and the same thing over again.

Other side notes-
Engine wont turn over from inside car with key in ignition. No fuses blown or anything.
The only way I can get it to turn over is jumpering the relay because I dont get ignition switch power to the relay.

I have searched using google and only seem to find a common issue is with the passenger side fuel pump.

Tomorrow I am going to using a little starter fluid in the manifold and see if it start to determine if its a fuel issue.

I guess my main question is will the car run with the coolant temp sensor not plugged in. I have tried to pull the EFI fuse and unplug the battery for 30 sec to see if that helps but nothing.
I have to pull the starter relay and jumper it

ZPEED

first thing u gonna do is get multimeter and test the battery voltage engine off and engine running and if u see the battery is 12 volt something while the engine is running then u need to replaces the alternator, 14 volt is normal for engine running..