PAM2804 Lithium-ion single cell LED driver fails
I had a pretty similar circuit 2 months ago, using TP4056 with PAM. Since, you are getting the output voltage, only other fault could be coming from lack of current. I would check if

Amperage and ESR of Inductor L1, are within specified tolerances (0.1 value of R1 will require atleast 1.5amp rated inductor, and LED you are driving requires a minimum of 700mA)
C1 is MLCC
C2, C7 could be Tantalum