That is a peculiar sound. Its sometimes hard to judge from a video but that sounds to me like the battery is ok but either .. 1) The starter solenoid is operating repeatedly but failing to turn the starter motor .. ie there is possibly a fault with the starter motor. or 2) The starter motor is operating but failing to turn the motor over .. indicating a possible fault with the starter sprag clutch. I'm surprised it started with a recharged battery .. maybe that was just a coincidence ..? Also, you won't hear the fuel pump priming because you have a carburettor model and they have a vacuum operated fuel pump. Finally, as its a monster, I should point you in the direction of UKMOC .. (uk monster owners' club). They're a helpful lot on there and also will be familiar with monster-specific issues.
Here is a link for the cable upgrade, I have fitted them and they do improve the cranking over http://www.exact-start.com/
That’s fab They don’t like standing still unused keep riding it Don’t forget your bins we like pics of your bins sand it’s a newbie rule