See this forum post for running games directly from a physical media. I don't think lr-pcsx-rearmed supports physical media though, for PS1 you need the Mednafen PSX core.
As far as Gamecube/PS2, I don't think the emulators in RetroPie (Dolphin/PCSX2) support reading the game from physical media.

@tzium

These are the soldering s you should check :
usb-solderings.jpg
See if there are no breakages in them.

If you only connect both your controller and keyboard, without other devices, do they work OK then ?

@RetroFloppy08 Another update: Added two more lines to the script so EmulationStation reboots itself.

@VictimRLSH not really enough CPU power, but it has enough GPU power - http://www.raspberrypi.com/mpeg-2-license-key/

then Kodi can play back DVD with hardware acceleration.

First, thanks for replying to me here and pointing out the error in my title. I want to try and use a portable disk-drive to play PS2 and Dreamcast games so I've updated it accordingly. As for why it's really for the same reason someone would want to play an NES game on the original cartridge, even if they're using a Retron 5 or some other device that employs emulation. It's what I grew up with and, since the purpose of this device is in part to relive that nostalgia, I figure it's worth trying to make work like this. I've heard elsewhere that, though PS2 games due to the raspberry pi's architecture are out of the question, Dreamcast and PS1 disks may still work so I'll post an update once I get the components and can test it out. Thank you all again for the replies.