Well Lenovo is a good brand.
They have the Thinkpad series which are known for great durability and build quality.
Not sure what cheap is to you though.
I bought my step sister a laptop for college recently and after going through many laptops I went with the Lenovo Thinkpad E430 because it was on sale (cheap) and it had nice build quality and performance for the price. Obviously it's not as high a build quality as the more expensive Thinkpads.
It could last around 7 hours on battery.
The Keyboard was comfortable to use and was spill proof.
The laptop never got too hot.
It had a rubber trackpoint stick for better mouse control.
The screen was 14inches which was large enough but small and lite enough to carry around without issue.
It came with an;
Intel i5 3.1ghz ivy bridge CPU
Intel HD4000 gpu
500gb of Hard drive space (7200RPM)
4GB of RAM (can easily upgrade to 8GB for around 25USD)
All for around 500-550USD.
Heck it even had a nice fingerprint reader for more security when logging in.
Also it has a nice plain look.
