It's also true, I think, that with a lot of reports claiming that a game won't work in this way, copy or mod protection may be the cause: comparatively few people reporting actually seem to be certain whether their setup can read subcode and hence defeat copy protection.
Does your game play Ok in a Playstation, Andrew? If so, then read my previous post and try this
If you're running 32bit Windows 2000, or XP (possibly also Vista and 64bit Windows - I don't know), get a copy of the wnaspi32.dll (linked in my previous post) and put it in your pSX folder. Open pSX' configuration and, on the CDROM tab set CD reading to ASPI rather than Auto or IOControl. Leave Subcode reading set to Auto.
If you're using Windows 9.x google for ForceASPI version 1.17 and install it. Then open pSX' configuration and, on the CDROM tab set CD reading to ASPI rather than Auto or IOControl. Leave Subcode reading set to Auto.
If you're using Linux, you only need to confirm that Subcode reading is set to Auto on the CDROM tab.
For all OSs, put a PAL Playstation BIOS (one with the 4 digit number ending in 2) in your bios folder and set pSX to use it.
Try playing the game from each of your optical drives. If one of them is an -RW drive, you have a better chance of this working. If your game works from any of the drives, you're in; if not, we're still not certain this is because pSX really doesn't play Parasite Eve 2, or whether your system doesn't read subcode, but, short of ensuring that you have a subcode-reading drive there's no way to be sure why.
And if not, you will have to use another emulator. A few people here have suggested ePSXe, but you don't want to use that; I can understand why - it's old and excessively complex to get working. You could try, as jonc2006 says, Xebra, another pluginless emulator that, like pSX, is still in active development. See here
for a link and instructions on downloading, and here
for instructions on how to use it. I've never used it myself because it's Windows-only, but it's supposed to work extremely well and possibly have even better compatibility than pSX. However, it is a Japanese emulator; if there are any forums supporting it, they're probably Japanese only. I believe the gui does display in English, though.