Check all the fuses on the motherboard.
Particularly the PS1 fuse is important for your case as it is the main fuse for the standby circuit.
If that's not blown but the console still doesn't light the red light, then it has a faulty syscon chip and you're unlikely to be able to fix that problem.
SCPH-10000_GH-001 SCPH-15000_GH-003 SCPH-18000_GH-008 SCPH-30001_GH-005 SCPH-30000_GH-016(V4) SCPH-30001_GH-010(V4)
2xSCPH-10190, 2xSCPH-10350, 2xSCPH-10280
"**** j0 hackers!"
-Sjeep (As seen on TOXIC OS ELF...)