some of the wiring may not have been hooked up right
replace battery cable ends
The battery is basicly used just to start your vehicle, the alternator is what generates your power once the vehicle is running. Which indicates you need a new battery, not an alternator. That is why you problem goes away after a jump start(boost). If it was the alternator the problem would not go away and your vehicle would have no lights and stall with no start. Either your battery is bad or the alternator is not charging.
check starter
The problem may be with your starter and not with the clutch.
If your car doesnt start, it could be the battery. But if the car starts and you unplug the negative cable and the car turns off, its the alternator.
The alternator might be the problem.
The alternator either has to be a factory original or a used off of a parts Rodeo,otherwise the alternator will not run.
it is your starter motor sticking, or could be your alternator but i think it is defo your starte motor.
if it is 10 years or older it would be the spark plugs
it could also be a carburetor problem
I'm no expert, but it could be a battery or alternator related problem.
It sounds like you have a break in the wire which connects your alternator to your battery, get it checked out.