If you do decide to put the battery live to the starter ... make sure it isnt in gear
always worth getting your battery checked i supose but ..
It sounds like your starter motor being tempremental, It sounds like its sticking or not engaging properly.
You can solve this, but it requires some knowledge of cars.
D/c the battery before doing anything though.
You can take the starter motor off and check for wear on the teeth, if their rounded or broken off it wont engage properly.
Also, the starter rotates as it comes out to help engaging, so if you turn it by hand it should be able to move out freely. They also have a one way clutch.
If possible take the starter apart, careful though theres a spring inside that can pop out.
The solenoid usualy seizes and it just needs a quick rub down with some emry tape, nothing too abrasive though.
It may not be possible for you do to so, but thats all it would be.