About the touchpad button I happened something similar to you; after a web search I found that I had only to push the button with more strength! Let me know if you fixed both!
Bye the way, this morning I updated my elitebook with the latest HP bios release! Then I reset the CPU to 100% I'll see...
I noticedthat with that setting the random shut down are almost gone; one thing only you have th right to have a fully 100% functional HP elitebook so contact the chat support for an model exchange or else!!
I'll be wating on twitter then :)
Hello, try to check if there is a feature to reduce the CPU power; if not go to the BIOS settings a see there if you may find something to reduce it. If not contact the chat support and use your warranty to ask for technical support!
This is the snap of my Power Assistant...
Install HP Power Assistant and click the advanced button bottom left; click on the left the arrow: "Processor Power Managament" and set the "Maximum Processor State:" bars at 70%; all will go right!