First step, you need to look at the standby and power leds on the
front bezel of the set and see if they reports a shut down error code
by way of led flashes. For eg, the PDP-433PE service manual states;

"7.1.2 SHUT DOWN/POWER DOWN DIAGNOSIS BY LED DISPLAY
When internal circuit abnormality and other operation abnormality
occurred from this unit, self-diagnose display function by STANDBY/ON
(LED) indicator is loaded.
Each NG point by LED blinking and a PD (power down) point are as
follows
SHUT DOWN
Operations : When a microcomputer detects abnormality, it turns the
power supply to OFF.
LED display : Green blinks
Number of blinks Name
1 Panel Microcomputer NG
2 DIGITAL-IIC communication NG
3 Dewdrop abnormality
4 Temperature abnormality

POWER DOWN (PD)
Operations : When this unit becomes the dangerous state, turn the
power supply OFF with the protection circuit.
LED display : Red blinks
Number ofblinks Name
1 Y-DRIVE
2 Y-DC/DC CONVERTER
3 X-DC/DC CONVERTER
4 X-DRIVE
5 Power supply
6 Address junction
7 Address resonance
8 DIGITAL-DC/DC CONVERTER

How to release the power down state
AC power OFF
$B"-(B
Wait for PD LED in the power supply module disappearing
(for around 30 seconds).
$B"-(B
Afterwards, wait moreover for five seconds.
$B"-(B
Return by AC power ON.
* After power down release, this unit rises up in the standby state."

The manuals have more elaborate details that you need to go through,
you surely need 1 else you'd be groping in the dark, dont go changing
caps blindly praying for a miracle..
You could try sharefx.com for the service manual. You need to register
and share a few before getting anyone to share with you ( like napster
or a regular p2p) I offer to try on your behalf should your request be
ignored. Let me know.

Jango