Download and burn a copy of UBCD
, burn it to CD (or even better, make a bootable USB stick) and you'll have most PC diagnostic tools needed, including RAM, HDD (manufacturer specific) and a load of other testing tools. Adding to that, it includes a suite of tools which can be accessed from a full GUI based Linux environment, which runs off a RAM disk.
It's simply a great little toolkit, which has helped me a great number of times.
Also, if you're planning to sell the TP, you may want to do a partition selective disk wipe, or at one which wipes all empty parts of the HDD, else the buyer may with very little effort be able to access most of any of your files which have only been deleted. Also formatting does not really actually delete any files, just the "address" to them. The UBCD site is down right now, but I believe there are selective wipe tools included in the suite.