If it matters, I had to drill out my battery connectors too since they wouldn't fit around the terminal.
You should put up some pics of your battery terminals and the setup if you can.
The vehicle should starts and run/function fine with the relay harness connected. It's gotta be your battery connections. Any poor contact and you will have no connection or a volt drop.
Hook up your battery without the harness connected to the battery.
Now the vehicle should be Normal.. Now turn on your headlight switch and go hold the pos and negative connections from your relay kit to the pos and neg of the battery with your fingers.
Your hids should work.
And to be clear, one of your factory headlight connectors is plugged into the relay harness right?