It'll boot up at idle, but crash at full load. Remember, only a part of the total 650w is routed to 12v rails, which runs cpu, gpu, hdds, basically everything. Also, 650w is energy draw from the wall, Even the best psu does not exceed 80% efficiency under realistic conditions. Not to mention effect of aging further cuts output.
A q6600 at stock 2.4ghz draws 105w, when oced, it can draw more than 200w on full load across all cores. Efficiency drops as vcore increase.
Hdd is also a constant drain. And while the dvd drive runs on next to nothing while idle, it can become significant when burning.
It's not just the 4870s the 12v rail out of the psu is powering.