1. The PS2 has firmware all right (And it is stored in ROM chip(s) and cannot be replaced). In fact, all computers (A console is a computer after all) have a firmware of some sort.
Originally Posted by .Spike.
2. PS2ESDL isn't runnable on it's own. You need to already have a way to launch homebrew (user-created) software. Look at some methods like FMCB and Swapmagic etc.
3. PS2ESDL currently cannot be run on the BC PS3. If you want to play PS2 games on your BC PS3, please use OPL instead.
4. Who knows? If that "other" loader that you failed to get working was USBExtreme/USBAdvance, then maybe.
(But if you cannot, you must have done something wrong). If you need additional help, you need to tell us your console's model number, the method you are using to launch PS2ESDL and whether your console has a modchip.
But I can say that PS2ESDL does work when launched from PS2LINK, Swapmagic 3.6 or FMCB v1.8b.
Unmodified SCPH-77006 with SM 3.6
SCPH-39006 with M-chip modchip, SCPH-10281 NA and refurb Seagate 80GB HDD
SCPH-10000 v1.00 with SCPH-10190 PCMCIA NA and SCPH-20400 HDD unit