The radiator could have some bad solder joints where the fins meet the top of the radiator.
You can pull the radiator and have it checked by a reputable radiator repair shop. If the radiator is a combination plastic and metal radiator, then it's probably gonna need replacing.
As far as the charging system goes. Your gonna need a decent digital multimeter/ voltmeter.
You need to check two places on the alternator for voltage. The main lug where it gets power coming in. It will be the largest wire going to it. Check to see if your reading battery voltage (12 volts to 12.8 volts) on a fully charged battery.
If no power, then you have an issue with the wire between the alternator to the battery.
The second place is what they call the exciter wire. It should have power when the key is turned on and attaches to the alternator either through a quick connect, or smaller gauge wire via either a spare connection or round terminal with a bolt. If no power coming into that wire with the key turned on, then it either has a blown fuse, bad diode (if equipped) or bad wire.
If your alternator has power coming to it from both places and it's not charging (reading 13.5 to 14 volts) then the alternator needs a rebuild.
But before diving into the wiring of the alternator, the quickest and simplest option is to check your fuses. If you find a blown one. Replace the fuse, start the machine and check the voltage at the battery. If your reading 13.5 to 14 volts then your good to go
I didn't notice whether you had the battery tested or not. If your just charging the battery, then having it not start the next day, then you could very well have a bad cell (small short) in the battery causing it to not hold a charge.
Easiest way I found, was to charge the battery fully. After the chargers removed. Let the battery sit for about 20 minutes. If the battery is in your machine disconnect the ground wire before charging and leave it disconnected while doing this test.
Check the battery voltage after 20 minutes. This should give the battery enough time for the voltage to settle from charging. Should read around 12.5 volts or so.
Let the battery set over night and check the voltage again. If it's still sitting right around 12.5 volts then the battery is good.
If it's dropped a significant amount then the battery has an internal short or bad cell.
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