the files actually don't need root access, although they are owned by root they should be readable (and in some cases writable) by all. just to make sure, try doing the following:
If that doesn't work, you can try the full uninstall/reinstall listed in the F.A.Q.'s at the beginning of this post, in the meantime I will get a feisty 7.04 32-bit Live CD out and try to duplicate your errors (I'm running nvidia as well, and if UT2k4 works for ya I doubt it is a video card issue).
sudo rm psx.ini
sudo touch psx.ini
sudo chmod a+w psx.ini
EDIT: I just booted to my feisty 7.04 i386 live cd, and after performing a few tasks (installed nvidia drivers via restricted drivers manager, restarted the X server, added the dfreer main repository) I did a sudo apt-get install psx. Other than one complaint about not being able to find libgtkglext1 (which is in the official repos, not sure why it doesn't grab it from there. I added a local copy to my repository to fix this), it installed without a hitch, and proceeded to run perfectly. Perhaps you have a corrupted BIOS file? That might explain why it seg faults immediately after asking for the BIOS file location. It could be a permission error on your BIOS file also, so make sure to do an ls -l on it.
finally, like i said try the full uninstall/reinstall of pSX.
FURTHER EDIT: I did happen to get this error:
It seems if the sound is misconfigured (for some reason, the second user has broken sound on the live CD), psx will abort (but not segfault, so I don't think these two problems are related.
pSX: pcm_params.c:2276: snd_pcm_hw_refine: Assertion `pcm && params' failed.
Aborted (core dumped)
Also, having looked at the ls -l info you provided, I realize that once again permissions aren't set right, (those folders really should be 777 drwxrwxrwx). I have fixed this in the new package, this only effects the i386 package btw. I don't think this was part of your problem but you never know...