Not really trying to defend Lenovo, but it's weird that you rarely hear about the good customer service, just the bad. Your situation sounds really painful and I'd extremely heated and probably be a lot more colorful in my language making this post. It's just the customer service issues that go by without a hitch are never really heard of. All but one of my dealings with Lenovo have been great. Extremely fast parts replacement, and nothing out of the ordinary. I had a t61 that I used probably 10-12 hours a day for a couple years when I was living with a girlfriend and had no desk to put my server/desktop. Heavy use all day, every day, on my lap. During this time I burned through 2 burners, 3 keyboards, 3 batteries, a hard drive, and a charger or two. Every time except one, it was no hassle; part on my doorstep the next day. I did have 3 year heavy duty warranty on it, even the battery. It wasn't onsite, but honestly, I don't trust anyone with my babies anyway.
The one time I had bad customer service was with a dvd burner that just completely stopped working. I even tried it in another t61. It was dead. Called customer service and she tells me to put in my diagnostic DVD. Are you serious? I'm not even trying to put a Diagnostic DVD in, if nothing else works, why would it? She felt kind of dumb then told me to get some Windows thinkpad diagnostic thing from their site. I didn't have windows. It came with SUSE, SLED 10. It was an option at the time and also saved me 89 dollars. I got really upset when she argued with me "Um, we only support windows." That's great. I don't need windows support. My drive is not working. Then she went on to tell me that they didn't sell linux thinkpads. This was an out and out lie and looking at my account should show her this. It came with linux preinstalled. After talking with her supervisor, who was very helpful, new drive, in the mail, next day. My problem with customer support lasted for one phone call.
I'm sorry this happened to you, but if the Yoga 3 pro won't do it for you, maybe sell it, and get something that does, but every large PC manufacturer is going to have lemons and customer service calls that never get resolved.