I would confirm that +5V is present at the input and output of U21 (MP5001DQ).
Also measure the voltages at inductors L1 - L5.
TPS3808G01, Texas Instruments, marking AVW, Low Quiescent Current, Programmable-Delay
Supervisory Circuit:
http://www.ti.com/lit/ds/symlink/tps3808g01.pdfLM73CIMK, Texas Instruments, 2.7-V, SOT-23, 11- to 14-Bit Digital Temperature Sensor With 2-Wire Interface, marking T730:
http://www.ti.com/lit/ds/symlink/lm73.pdfhttp://datasheet.octopart.com/LM73CIMK-0-National-Semiconductor-datasheet-8326679.pdfST1S32, STMicroelectronics, step-down switching regulator, 2.8V - 5.5V in, 1.5 MHz, 4A, 8-pin:
https://www.st.com/resource/en/datasheet/st1s32.pdfST1S31, STMicroelectronics, step-down switching regulator, 2.8V - 5.5V in, 1.5 MHz, 3A, marking 1S31, 8-pin:
https://www.st.com/resource/en/datasheet/st1s31.pdfL6928, STMicroelectronics, synchronous step-down regulator, 2V - 5.5V in, 800mA, 1.4 MHz, 8-pin,
https://www.st.com/resource/en/datasheet/l6928.pdfMP5001DQ, Monolithic Power, 5V, 1A - 5A Programmable Current Limit Switch, marking W5xx, QFN3x3-10:
https://www.monolithicpower.com/pub/media/document/MP5001_r0.94.pdfADM6710PARJZ, Analog Devices, Low Voltage, High Accuracy, Quad Voltage (adj, 3V, 1.8V, adj) Microprocessor Supervisory Circuit, marking MAV, RJ-6:
http://www.analog.com/media/en/technical-documentation/data-sheets/ADM6710.pdf74LVC1G07, Diodes Inc, single non-inverting buffer, open drain out, 1.65V - 5.5V in, marking UNywx, 5-pin:
https://www.diodes.com/assets/Datasheets/74LVC1G07.pdfTPD2E009, 2-Channel ESD suppression diodes for 6Gbps eSATA, marking 4T, SOT-3:
http://www.ti.com/lit/ds/slvs953b/slvs953b.pdf