Here's the full game (both CDs) for download:
• Parasite Eve (NTSC), Disc 1 - 316 MB
• Parasite Eve (NTSC), Disc 2 - 332 MB
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.
Make sure you're using the latest version of ePSXe. The slighlty older version 1.7 has a bug where Parsite Eve locks up at the point when you do the disc swap to switch to disc 2.