In addition to memtest and the hard drive test suggested by Rich, I would also run Prime95 for an overnight.
I also start removing the unwanted software and trialware as soon as I get it out of the box. That alone tests a lot of normal operations. When you start loading your own programs you will be testing the DVD drive.
I also start going through the Device Manager item by item, noting the component manufacturer and model number and current driver
. I can google the component to see if others are having any issues, get a bookmark on the manufacturer's website driver section, and have the list of components handy.
Also check the operation of video by testing the graphics using Windows 7's 3D games set at the highest levels, play with the Desktop Personalization settings and backgrounds, run WEI, and run any video intensive progs you have.
It was only after my daughter owned her laptop for a while (which we also found for $450 at the time) that we discovered that the on-board sound chip on her Persario did not have the capability to have a "Stereo Mix" device, regardless of driver. So you might take some time to look at all those Hardware and Sound Settings and see that all is there that you expect to be there.
Other than that, just play with it!