i can think of 3 things that will cause those kind of problems.
1. main power and earth leads from the battery, check all connections are clean and tight.
2. starter solenoid, try starting it via bridging the two main terminals with a screwdriver make sure you are in neutral as it bypasses the safety start system if it spins over better the solenoid is on its way out.
3. starter motor, the brushes and/or the armature could be worn so might have a dead/damaged spot so when it stops in that position it draws more power and cant spin up properly so needs an overhaul.
if 1+2 are ok 3's your problem
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