...I click the third file in the folder...
A lot of the English patches create a new executable file, which you can open to run the game in English. The original executable is still there in case you want to run the game in Japanese.
What you're clicking on is the original .exe. You want the "th06e" one.
Also, EoSD wasn't designed with non-japanese computers in mind at all, so it has a lot of trouble running on them (mostly due to Japanese filenames). Please read the "Japanese Language Packs + AppLocale Tutorial" thread, it is a sticky in this same sub-forum.
I can't remember if the EoSD english-patched .exe can run without AppLocale or Japanese regional settings, but if anything, the error you're getting is probably the game not finding the files it needs to run (again, due to their names being in Japanese).
Ah, yes... AppLocale does run on Vista, but to install it you'll need to run it as admin. Open a command line as admin (right click on the Start Menu entry > Run as administrator), then go to the folder with the AppLocale installer, and open it form there.