These steps probably won't catch every last little thing; but they ought to be a good start. First, test the screen. There are programs that can do this, or you can just use paint. The idea is to fill the screen with pixels of all one color, once with red, once with green once with blue, and see if you have any stuck on/stuck off pixels. You can then test the optical drive by using it for its intended purposes. Burn a CD or two, watch at least part of a dvd. If you want to be sure about the ram, run memtest86 through some or all of the tests(most of the time errors are caught well before the end of testing if they exist; but i f you want to be sure run a full round of testing). Then, just because laptops tend to have cooling issues, do a burn in with prime95 or similar for a day or two. If it can keep itself acceptably cool and stable through that, it is probably alright. I don't know what sort of understanding you bought the battery under; but you will probably want to test battery life as well.