I will take a look at the fpf1320. How can i measure it?
First it's visual inspection if it's not cracked. Even nicked corner may kill it. Second it should output 3.3V when run with no micro SD card, when running with SD card it should drop to 1.8V after a short moment. However it may not also if CPU is bad. You can measure it across capacitor circled red on the photo. On newer revision boards IC is placed on opposite side of the board and this capacitor is turned 90 degrees.
As of verifying if MXL7704 is the problem (if some of output voltages aren't right), you can measure resistance to GND on 4 power rails before, and if there are shorts, after desoldering it. Resistance on 1V1 rail should be 10 to 100+ Ohm depending on RAM type on the board, Samsung resulting in lowest. VDD_core should be like 25-200 Ohm. The rest in kOhm range. If short(s) remain after desoldering MXL7704, most likely CPU is bad.