I would suggest a new PSU, as 700W is pushing it even with a brand new unit (SB-E + 580 + spinup of 6 platter drives = lots'o'amps!), and after 6 years your unit's capacitors have degraded enough that it's quite likely unable to produce those 700W.
Furthermore, PSU's have come quite a ways in the past few years, especially in terms of efficiency and voltage stability (ripple control).
One unit that I personally vouch for and can recommend without hesitation are the NZXT HALE90 models, particularly the new HALE90 V2 units. They are about as solid as it gets, well priced, and the internal construction is simply beyond what I've seen in almost any other consumer PSU.
I'm sure I'll get a backlash for this, but I would completely avoid Corsair units. They're overpriced, offer middle of the road performance for top-shelf price (they're like the Grey Goose of PSU's!), and I know of multiple AX1200i units that have (literally) spontaneously combusted.
Don't look at the brand, look at the OEM, it will tell you so much more....
I think the HALE90 V2 850W unit would be ideal, personally...