I had the same issue with our 722 last year. After sending it back to Sound Devices, this is what they found:
"The technician working on this unit has determined the fault lies in a A Ball Grid Array FPGA. Sound Devices does not have the facilities to reliably replace this component. I have confirmed the fault.
Cooling this component allowed the unit to power up. The unit remained operational over the weekend and has now powered on after being powered down for three days.
As this was not a technical repair, we must assume the fault may return at some time in the future. This leads me to recommend the option of replacing the main board set with a new production set. The new set carries a one year warranty against manufacture defect.
Additional replacement of the CH1 input XLR connector (insert pushed in, separated from the body) and Headphone Volume Potentiometer (left side scratchy) are recommended.
As the unit requires hardware updates to bring it to the V2.0 level, these updates will be applied at no charge and flat rate labor charge will not apply.
Should you choose not to proceed with installation of the new boards set, we can, if you wish, continue with the updates and XLR and HP pot repairs with parts charges only. Or we can return the recorder in its current state.
Of course the unit would not be warranted for the FPGA issue should it arise again."
PN 1605 - 722 Tested PCB Assembly US$836.42
PN 113 - XLRF connector US$3.84
PN 3425 - Potentiometer US$0.96
We decided to have it repaired.
Now I'm not sure that this is the problem that you are facing, but just letting you know what you could potentially be in for.