Do you still have everything on the old computer? If you were copying everything over to the new one, the easiest method to clear everything would be to re-install Windows (in the custom setup options you should be able to delete the current partition and re-create it). That will make sure nothing gets left behind. If you were moving files over to the new computer, make sure you move them all back before re-installing, if you don't otherwise have a backup.
If you just need to make sure everything you move or delete is gone, you can use a program like
Eraser to securely delete files and/or wipe the un-used parts of the drive (to take care of possible fragments left from already deleted files).
Run this after re-installing Windows, and nobody would find any personal info even if they went looking for it.
There are programs that can be run from a bootable floppy, CD/DVD-R or USB drive which will wipe out the entire disk, but that would also take out the recovery partition, required to re-install Windows (though HP does have a program to let you burn a set of recovery DVDs).
