Plumbing – Dishwasher supply line leak

I think what is leaking is the drain. Does it look like the object sticking out to the side in the below picture? If so, this is used to drain water from the house side of the supply when the valve is off.

It sounds like you over tightened it in the first place which started the leaking. If you've broken only the cap, you might be able to find a replacement. If the stem and threads are damaged, long-term you will need to replace the entire valve. As a short-term fix, you just need to block it some how. Marine epoxy is handy for emergency plumbing repairs.

You need a new washer inside the loose connection. The tank/hose connector is 7/8 inch (in the States). An "O"-ring of proper size will do. I've substituted the washer from a garden hose in a desperate situation. But it would be wise to purchase a flat washer specifically for the 7/8 inch tank connector.