My 1997 LeSabre Limited has full power and good Battery but will not turn over

I simply parked one evening and came out the next day to find it would not turn over. I have tested the battery which is good, I have even replaced the
battery. I have removed the starter and had it tested and it is good. I can do the old screw driver across the terminal trick and get the vehicle to start and run for aprox 60 seconds and then it shuts down?
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