For starters you need to make sure you are putting it into Factory Service Mode(FSM) properly. Assuming your FSM device works, you aren't doing it properly.
1/The PS3 needs to be turned off and disconnected from power
2/Connect your FSM device to the right most USB port
3/Reconnect power to the PS3
4/Press the power button, then immediately (less than a second) press the eject button
5/The PS3 should then automatically turn off
At this point your PS3 should be in FSM. Now you should NEVER attempt to upgrade PS3 firmware through FSM (causes a brick), you should only attempt to re-install the current FW or downgrade. Your best bet should be at installing a retail firmware at 2.20 or lower. I would recommend 1.90 if you want to be sure not to accidentally upgrade, because CECHE01 models usually ship with that Firmware.
1/ Now get your FW update of choice(1.90) and rename it to "PS3UPDAT.PUP" and copy it to the root of a blank USB stick,
2/ Get your special Lv2diag.self (which ignores missing Bluray Drives) and copy that to the root of the USB stick you copied the FW update to.
3/ Plug the USB into the right most usb port on your PS3
4/ Turn the PS3 on (the PS3 won't display anything to the screen), and watch the HDD indicator. It should start flashing soon after turning on, this means it is installing the firmware.
5/ Usually the PS3 will turn itself off when finished, but if a long time (30 minutes) has passed and it still hasn't turned off, check the HDD indicator. If it isn't flashing, then it probably isn't doing anything, so it should be okay to turn off. If the HDD indicator is still flashing, then it's time to be concerned.
Now turn the PS3 on, hopefully your PS3 will boot into the XMB(and say FSM in the lower left hand corner in a big red box). If not upload the log file from the firmware install here.
If you did successfully boot into the XMB, then your PS3 is working, and now we need to exit FSM.
1/ Delete the files from the USB you used to install retail FW 1.90. And put on the root of the USB the Lv2diag.self which is used to exit FSM.
2/ Turn off your PS3, and plug the USB into the right most USB port on your PS3
3/ Turn on your PS3, it should turn off automatically after a few seconds
Your PS3 should now be running retail FW 1.90, you should be able install any FW from here. But do some research for installing FW on PS3s without Bluray drives.