If it's under warrenty, then there is no need to diagnose it yourself.
Even if you could, there isn't often much that you can do about it (assuming it's hardware related).
The RMA process can be found here. There are 'continue' links on each page.
Desktop: AMD Phenom II X4 965 @ 3.5GHz, Sapphire Vapor-X HD5870, ASUS M4A78T-E, 8GB Kingston/Mushkin DDR3-1333, 256GB OCZ Vertex 4, 2xSeagate Momentus XT 500GB Hybrid Drive (RAID0), ASUS Xonar Xense, Corsair HX750W, Antec Nine Hundred, Windows 7 Professional x64.
HP Touchsmart TM2: Intel Core i5 430UM, Hitachi 250GB 7200RPM HDD, ATI Radeon HD5450, 8GB Samsung DDR3-1333 (CL9), Windows 7 Professional x64.