Why is there electricity flowing through my VGA and other connectors?

It sounds like your laptop has issues with a ground, since the voltage on the VGA connector is floating high. You should not have gotten an electric shock, since nominal VGA signaling occurs at 0V and 0.7V. If possible, open the laptop, and try to see if any components are electrically shorted to the laptop chassis and/or other connectors.

If you only experience the shock when the charger is connected to the laptop, then you should stop using the charger immediately and get a new one. Check the charger itself for ground faults. If you are using an ungrounded charger, there may be an electrical fault in the actual socket. Start with the charger, and work from there.

Again, there is no voltage in the laptop which is high enough to shock you. I have not seen any laptop chargers provide a DC output higher then 18.5V. Look into the charger or any short circuits (either in the laptop or charger), but again, since you're getting shocked, ensure that your charger is not the problem.