I think this is the best option. You can download practically anything from a torrent website. The torrent program that most people seem to prefer is uTorrent. Once you download the torrent program, you can then partake in downloading torrent files. There are tons of websites out there that host thousands of torrent files. I have a few popular ones listed here. Simply put "parasite eve" into the search and that should take you to its download. Or to save you some trouble, here's a direct link to a Parasite Eve torrent:
• Parasite Eve (NTSC) - 1.06 GB
Parasite Eve is a very large download. It could take several days to even over a week to download it. You'll need to leave your computer on overnight.
You can play Parasite Eve right on your computer with a Playstation (PS1) emulator. I have the best ones for download in my emulators page. And if you need assistance with the Playstation emulator, check out my emulation help site, Video Game Emulation for Newbies, for help.
IMPORTANT NOTE: ePSXe v1.7 (the latest version, and the version in my site) has a bug where Parsite Eve locks up at the point when you do the disc swap to switch to disc 2. You need to use ePSXe v1.6, as it does not have this bug. If you're like me and you always want to be using the newest version, at the point before the freeze you can transfer the save state or MCR in-game save to v1.6 temporarily (just a simple copy & paste), then after the disc swap jump back to v1.7 to finish the game.