The standard things to check are the connectors, both at the motherboard and at the display panel itself. The latter in particular are somewhat infamous for developing poor contact over time. Often, simply pulling out the flex cable and reinserting it will fix things (for a while, at least). Even better: Gently rub the exposed conductor traces with a pencil eraser prior to reinsertion.
Whatever you do, avoid touching the exposed contacts, otherwise the problem will recur very quickly.