Are you sure that you're downloading the proper, full rom for the phone? Many of the roms are almost 1GB apiece for a full OS replacement.

If they're HTML files, then it sounds like all you did was copy/paste the URL links onto the SD card... which of course won't work.

 

Try my CM 11 modified that I posted, either the 12/7 or the 12/12 will work the same. If you can't get that one to work, I don't know what is going on, it is guaranteed to flash and run properly if all is functioning as it should.

http://androidforums.com/boost-mobile-galaxy-s3-all-things-root/804415-official-cyanogenmod-11-nightlies.html

 

Same can be said for my stock build. If you're flashing and downloading correctly, then it's guranteed to flash and run properly. Sounds like you may be downloading the link, as someone mentioned. Check the md5 either on the dev's OP or the site itself that you get it from. Also, what CWM are you using? Some cwm's have a hard time reading the sd card on this phone. Try Philz if you haven't already. Flash it through Odin in download mode, reboot to recovery, and try to mount usb storage that way.

 

I have yet to try this new Philz Recovery. I'm still using TWRP. With all this good talk I keep reading about, I may just have to give it a try.

This is the TWRP for Odin I'm still using-
Dev-Host - recovery.tar.md5 - The Ultimate Free File Hosting / File Sharing Service

 

I can pretty much personally guarantee you'll love Philz. I have used TWRP exclusively for over two years now, until being introduced to Philz. Not going back anytime soon, especially since TWRP 2.6.3.1 was a complete disaster (2.6.3.0 was very solid though, definitely not knocking TeamWin, they are just now in second place for me).