I have a Gateway Destination, and have yet to have a problem (it's 10 years old). I try to avoid HP (used to work for them and their manufacturing is garbage now). I have had numerous issues with my HP.
Name brand computers in general are pretty much junk
Dell, Gateway, Compaq, and E-Machines are BY FAR The worse
HP is a close second (some company as Compaq)
Build your own or have one built.. or go with a nice offbrand such as Acer or Asus.. they pay much more attention to quality and spend less of their money on advertising