I am after at least a dual core laptop..
Ram doesn't really matter.
HDD Doesn't really matter.
Should have good battery life.
Screen should be free from blemishes and dead pixels, and must at least a 15.4" screen, would [prefer a 1.6" or a 17" or higher.
Should have no faults and be in good cosmetic condition.
Also some warranty would be a nice added bonus.