One of the best ways to diagnose a fault on the PS3 is using the syscon tools.

Some consoles do not support full Syscon (check here). Even if full syscon does not work, you can do the Putty steps below to at least read out some basic error codes.

Check your model number by looking for it written on the motherboard, and your Model (left hand column) is the writing written on one of the chips on the motherboard.

Strip down the console to just the motherboard, and add the power supply back on to the console, and the power button strip.

Get a UART to USB device such as a CP2102.

Press Windows + X, then M to open up Device Manager. Then expand Ports (COM & LPT). Connect the UART to USB device to the PC and watch which new port appears in the list. Take note of this. Something like COM6 for example.

Download and run the Windows64_gui_ps3_syscon_uart_script.exe on your PC to open up the GUI.

Select the COM port from the list.

For the mode, if your PS3 had the DIAG pin you needed to solder to ground, the mode is normally, but not always, CXRF (Internal command mode, baud 15200), otherwise tru CXR (External command mode, baud 57600)

Connect the original 12V power supply to the PS3, and the white low voltage ribbon from the power supply to the console and power on the console.

Press the power button on the PS3 to turn it on. This gives you usually at least a few minutes to then run the UART diagnostics.

Click the Auth button a few times until it successfully authorises.

Once it has worked, in the Command box type ERRLOG GET 00 to read the first error, then ERRLOG GET 01 to get the next one, in hex, up to 1F, so 09...0A...0F...10... and so on.

If you cannot get it to authorize, your console might not support the Auth command. Instead install Putty and then select Serial, the COM port, and the right speed (57600 or 15200).

Connect up just the ground and RX wires (receiving from PS3 to PC), click Open in Putty, then turn on the console. It should report out what is wrong.

Get your code and compare it to the codes here https://www.psdevwiki.com/ps3/Syscon_Error_Codes.

For example, the above Power Off State Fatal 36, is boot stage 3036, meaning a bad RSX (graphics) and or CELL (CPU).

In this below example, the error codes are 3034 (3034 CELL / RSX Communication Error) and 4402 (CELL or RSX). This would be a candidate for reflowing the RSX chip.

Once you have done any remedial work to fix any issues, you will have to remove the DIAG ground wire otherwise the console won't boot, and then test booting a few times in order to generate any new error codes.

For example, a PS3 that came in with 3034 for thermal ball fractures, after reflowing the RSX (GPU), then turning on once without reassembling, and re-reading the error code from 00 you can see the new error code is 1201, which is the RSX (GPU) getting fixed.

After rebuilding it fully with fresh thermal paste and the heat sink, the console was back up and running.