Ok, symptoms so far:
ePSXe dies in Chrono Cross any time you try and use an element, changing the bios didn't help, changing plugins didn't help. In addition, three different disk copying programs are having trouble reading it (CDRWIN and IsoBuster are dying at 87% and BlindRead apparantly has to work around some bad sectors somewhere).
Although it seems unlikely, the directory structure that turned up in explorer is correct, or at least is consistent with what I get when I try and explore it (and I have a working ISO). The majority of the content on the CDs must not be stored and read from files, but read directly from specified sectors of the CD.
My guess would be either A) you have a faulty CD (scratched or otherwise) or B) your CD-ROM drive is having problems. To further diagnose, I'd suggest trying to make an ISO image of the second Chrono Cross CD with CDRWIN and/or IsoBuster to see if they can read it correctly, and to try running Chrono Cross from the CD instead of from an ISO (although, if the drive can't read the CD correctly, the cd plugin will likely either lockup or cause epsxe to crash when it tries to read from that same spot). You might also try running with a CD plugin that lets you disable caching, like Pete's, to prevent a readahead buffer from running into the bad spot early. Those suggestions should help you narrow down the problem further.
Oh, as a final thought, you can get a program called WinSFV at
http://www.peregate.com/anvil/sfv.html that you could use to check against your ISO image to see if it's damaged. To use it, run it, navigate to and select the directory that has the Chrono Cross iso, hit next, change the checksum file (give it a unique name, like checksum.txt), select the chrono cross iso, then hit next. It will take it quite a while to calculate a checksum for the iso, which will be stored in checksum.txt when it's done.
I made my image in IsoBuster, and as I don't have BlindRead I can't make another image in that, but my working .BIN file (736,651,104 bytes) has a checksum of A07898CC.