Start with the memory. How new it is is irrelevant, electronics can fail at any time. Download Memtest86 (http://www.memtest86.com/),
burn to CD, and run no fewer than 3 complete cycles on each stick of RAM individually in each slot. Follow that with pairs, alternating order and banks between tests. If there are 4 sticks then finish up by testing all 4, changing the order of the sticks between tests. Be prepared for this to take a long time.
If, by chance, you are overclocking, return everything to stock clocks and voltages.