This is Rewritten version as the first wasn't quite specific. I bricked my ps3 slim using the e3 flasher. I successfully downgraded from 3.73 to 3.55 and was experimenting with it and install a Modified pup and got bricked.
Of course my mistake is that I did not backup my 3.55 dump and as a result it's a unrecoverable brick until I came up with a method to fix.
This has worked on my ps3 slim and Fat, and many others who are a victim of accidental brick by using e3 flasher. E3 flasher is a great product and offer many awesome benefits in owning one of these.
Depending on your brick type may effect differently for everyone, Ultimately I believe it should work for most. In the process of re-flashing your bios I will provide my own customized BKPPS3 bios I made, this alone will not fix your issues but is important process to unbrick
For this to work you must have a good bios backup without errors that your created from your console. (does not matter which FW you backup as long its from your console.)
First thing you would need to do is solder the wire SBE to PAO TRISATE as everyone knows that's how you reflash the backup bios, the purpose of this wire is to by-bass the original start up and keep the ps3 on for a reflash. If you don't know which to solder get with e3 website under downloads, they have pictures which helps.
Ok now download my mod BKPPS3 which link is below and flash it to your console, once its done shut off ps3 and unplug it, move all switches to (PS3 mode) 1-6 down. Turn on ps3, your PS3 should start but no video/audio or HDD activity if so continue Next Step.
Remove your SD CARD from TF and delete all files on it, put your working backed up bios AND E3 flasher text document and load it on SD card to TF board. Have the number one switch up and rest is down to reflash your ps3 so 100000 and push start. Finish that and LEAVE PS3 ON (DO NOT TURN OFF)!! AFTER REFLASH YOUR OWN BIOS!!.
Remove your SD CARD and put e3_Downgrade.bin file WITH your working BIOS and put it on. Push reset button 3 time before and after you change the switch settings to 000001. Push start and downgrade bin should be installing. If all went well after successfully installing E3_downgrade.bin continue with original downgrade tutorial which would be inserting JB Dongle etc..
This may be confusing I am sorry having hard time explaining this so bare with me thanks. I am trying to help everyone.