Sorry, I don't have a solution, but other symptoms on my Toshiba Satellite A105-S2051 (model PSAA2U-049018).
Upon pressing the power switch, my unit turns on (all LEDs on) for ~2 seconds, then cycles off by itself, then back on again (six times total). It happens the same with or without power adapter, with or without battery, and with no hard drive, RAM, optical drive or other devices attached.
I have performed all of the suggestions presented here and elsewhere, with no changes in symptoms.
One clue is that this unit has provisions for 2 devices under the rear cover, adjacent to the RAM connectors.
One has a connector about 2" long with maybe 70 pins (marked with "63BJB"), and the opening for the mystery module is about 2" wide (squarish). Two wires (black and white) are present with round connectors are present but disconnected.
The other opening is about 1.5" square and has a 12-pin SOIC-type connector and again two wires, this time with a push-on 2-pin female connector. There are also 2 female screw lugs, presumably to mount the mystery module to the motherboard beneath.
These modules could be wireless (Wifi, bluetooth, etc.) or other configurable items.
I'll try to include photos if this board allows, but I don't see a button to include photos at this moment. I've posted a photo at:
http
/jamesheiresconsulting.com/images/IMG_2868.JPG
My question is if either of these 2 mystery modules are required to boot to BIOS/POST.