i remember it used to require a specified PS1 game to act as a boot disc, pretty sure things have changed since then i read around the time the PS3 was hacked that not only did the PS3 hack lead to being able to sign PSP stuff, but also PS2 which lead to the autobooting freeMC stuff *iirc*,
now to clarify for the people saying you need a action replay it was only the action replay max that ran homebrew from the USB that worked to install freeMC(this was the back in the day name) so it wouldn't help to get the action replay V2....but as the OP said he can't play discs he would probably need to either install on a friends PS2, use the PC memory card adapter or buy a memory card with it pre-installed which imho would probably be the cheapest/easiest option