I reread your original post. There are some things you MUST do or you will chase this problem around for a long time.
Check the battery acid level if it is not a sealed battery. If it is ok or slightly low add water, and fully charge the battery. If the battery is very low on acid, or empty, or the case is bulging, DO NOT ATTEMPT TO CHARGE IT! The battery is bad, and can be a danger. Get a new battery.
Unless the battery cables are new, get new ones. Positive, battery to solenoid and solenoid to starter. The battery ground to engine must be replaced too, and any other ground straps. battery to frame, frame to body, etc. The cables can be a hidden problem that must be eliminated before any other checks of the electrical system. Cables are cheep compared to starters and alternators, both of which have been replaced by well meaning people when the cables are the problem.
Once you have good cables and a fully charged battery, check the voltage across the positive and negative posts. You should have 12 volts minium. Have someone crank the engine, if during cranking the battery voltage imediately drops below 10 volts, the battery is bad. If the drop is gradual, there is a good indication the starter is the problem.
If the battery passes these tests and the engine can be started, check the charging system. With the engine running at about 1000rpm and all accessorys on you should read 13.7 to 14.2 volts. If you have that, the alternator is ok. If not then the lack of proper charging must be diagnosed. More on that later.
Remember, all these tests are based assuming the cables are good.
check each system one at a time.
GOOD LUCK.
Let us know what you find.