Hello.
I tried downloading PsoBB Eden on my Windows Vista 7 laptop, and I have everything I need for the installation.
But when I UNRAR all my files, Psobb.exe either does not exist, or it's there for 2 seconds and then it disappears.
I've tried the installation twice, and I've also tried downloading the Psobb.exe file itself, and it still does not work.
Any suggestions?

That happened to me a few times. I can't remember exactly how I fixed it. Try

-refreshing the desktop/wherever you unzipped the files to
-restarting your computer
-saving the .rar to an external drive and unzipping there
-try unzipping in many different locations until one shows up. Then manually drag it to where you want it to end up.

It'll be your antivirus that is quarantining the file.

To fix: Temporarily disable your antivirus realtime scanning. Unpack the client and add PSOBB.exe to your antivirus exceptions and then start realtime scanning again.