Brand new Hp probook 6540b blank black screen after battery dying fan also works over time any ideas to fix?

I have had this. Unplug the laptop, take the battery out and hold the power button for 30 seconds.

HP told me this was caused my "excessive charge on the mainboard"

The above process drains the charge

If you need a 9-Cell or 6-Cell battery, try this one the best choice.
http://www.battery-center.net/hp-probook-6540b-battery.html

I suggest you return this HP back to the supplier for warranty repair or replacement. If you try to fix it yourself you most like void your warranty.
I would only attempt to fix it when the laptop is out of warranty.