Push power button, turns on 10 minutes later :-/

i would check carefully the motherboard with a magnifier for a defective capacitor or coil even a resistor that appear bubbled or not looking as the other ,mostly around the power section for the front panel

There is no physical deformation or damage that is obvious. The PC tech I took it to checked the MB out with one of those mad scientist magnifying glasses.

Are PSU's known to have a charging time? Say its completely discharged.. maybe it needs to charge back up before starting up?

Usually a PSU turns on instantaneously. What PSU model do you have?

When you hit the power button, does the monitor display anything?

http://www.microcenter.com/product/349702/EL_Series_400...

There is no activity when i press the power button, computer or monitor.

-power supply has a interface to the motherboard that indicates that the power is good. The motherboard can keep a signal to the CPU low until it gets that signal indication of power good. mostly, you can get a delay of 3 or 4 seconds. longer times indicate a problem (pulling too much current, bad powersupply,...)

-some BIOS will try different settings and do a bunch of reboots when overclocking fails. I guess that could take 10 mins.

-Lots of lower quality supplies fake the power good signal, some actually implement it.

-I would check my connections from the power supply to the motherboard and any connections from the power supply to graphics cards and other devices.

if you think you are pulling too much power, you can reduce over clocks, disconnect devices to see if that helps.

-video card can go bad and pull too much power also.

otherwise I would have my power supply checked. (most likely cause)
edit: you indicated you leave the system on all the time. You could have a failure in the startup circuits of the power supply that would not be detected until you power cycle.

try to borrow a psu with more power to test your start up time and if your system start in less then 60 second then you need another psu