No, UEFI not being enabled would not cause the board to fail. I installed WIn10 on an old Thinkpad T61p which doesn't have UEFI.
Funny you're having issues, because a friend of mine was having issues with his HP laptop as well...which has similar symptoms as yours. Though his apparently may qualify for a repair because they apparently had a recall on them, but he hasn't looked into it yet. He had issues on both Win7 and WIn8, and ended up getting it working back on Win7 for a short while. THen he tried upgrading to WIn10...and boom - started happening again. Tried going back to Win7, and wouldn't boot anymore.
Just another reason why I shy away from HP's consumer line...