Seeing as you have a multimeter you could test the rest of the voltages / plugs (at least the 24-pin and 8-pin):
http://en.wikipedia.org/wiki/ATX#Power_supply
Best step may be to find a spare PSU to test it on. If it's a crappy old PSU unplug as much as possible before you try it (even HDDs, DVDs, etc).
I might also try running the system with no RAM in at all and no video card in at all (as separate tests). I'm not sure of the current state of BIOS beeps but once upon a time you'd get beeps for a system with no RAM in - and I *think* the same with no video card in (been an age since I tried it).
Then it's down to the usual suspects - you've tried a new mobo so you've reseated the CPU and heatsink so that only really leaves trying the system with the mobo outside of the case to rule out a short (which you may have also already done...). Sometimes I've seen boards that won't boot because of a dead CMOS/BIOS battery though that shouldn't be happening with a new mobo...
Would also do as much of a visual inspection of the PSU as you can without voiding the warranty (might be something showing on one of the cables, doubt you can see much of the internals without opening it up and voiding the warranty though).