Switch won't charge or output when docked.

[yankii]

I tried a bunch of official chargers and cables, all of which work with my other Switches, but my V1 refuses to charge via anything except my MacBook's cable [which means it won't charge nearly as fast], and it won't output to my TV when docked. The dock, which works with other Switches, starts flashing green rapidly when I insert my V1 into it. I tried a few other official docks too [all functional], but the problem persists.

Is there a fix for this?

 

[thesjaakspoiler]

When the led of the dock flashes green rapidly, it means it could not properly dock with the Switch.
Start by cleaning the USB connector with some alcohol.
If that does not work then likely there is something wrong with the connector.
Sometimes it detaches some of its pins from the motherboard.

It needs special pins for negotiating fast charging and for video output you also need a bunch of pins.
The power pins are present in pairs so if 1 pins gets disconnected, it will still be able to charge slowly over the other pins.

A good repair shop can fix this for you.