The link below is for Amazon. The price listed is $999 but I was able to drive to Best Buy and pick one up for $200 cheaper at $799 just last week.
Amazon - Lenovo IdeaPad Yoga 11s 11.6-Inch Convertible Touchscreen Ultrabook - Intel Core i5-4210Y Processor, 4GB Memory, 128GB SSD, Windows 8 64-Bit (Silver Gray)
We also had an Asus with a bum screen. I chose a smaller 11.6 inch screen on the Lenovo since my daughter lugs her laptop all over so she needed something portable and smaller screens or less prove to break.
I researched it a lot and this is the best convertible model that I could find anywhere close to this price. It does not have the 8GB (only 4GB) of RAM that you were looking for but the performance is excellent with an Intel i5 processor.
The best part about it is the design where the screen can flip 180 degrees backwards to convert into a tablet. When the screen flips back it disables the keyboard and turns into a tablet. You can also use the touchscreen even when the keyboard is not disabled.
