Why won't the GFCI-protected devices in my kitchen work even though they seem to have power?
Is this a new outlet where there was not a GFCI before?

Was the unit working before and suddenly stopped working?  

There seem to be too many downstream devices on the load side of the GFCI.  I would have expected this list of devices to be on at least 3 circuits.  That may explain why there still live circuits after shutoff to the GFCI.

In general, GFCIs won't reset when


They are wired incorrectly (power to load terminals)
The load side is ground faulted (current leaving the hot side does not fully return on the neutral)
The GFCI is faulty


To isolate the GFCI from any downstream problems, disconnect the load terminals and see if it will reset.