I don´t know if this is helpfull or not.. tried the hdmi in 2 different full hd tv. the image is always bigger then the screen. i´m not able to see the little apple logo in the upper left side also the dock is almost fully hidden. thanks
Have you the latest version of Mavericks 10.9.5 installed?
5 minutes to boot are too much. There is something wrong.
Prerequisite; all kext in S/L/E. Be sure you have no Extra folder on the root of the disk, should it be the case remove it (or move it in another place). Reinstall the kext with kext wizard, repair permission with "Disk Utility", rebuild cache with kext wizard, use DSDT Layout1 and reboot.
Be sure to perform every step
Have you tried to plug a device (Speaker, headphones)on the green output selecting "internal speaker" as output in "System Preferences/Audio"?
How did you test if audio is working? I suggest to play a youtube video.
You can not have internal and HDMI audio working together, either one or the other. If you see the volume icon in black, as I see in your images, you are using internal audio. For HDMI you have first to chose it in "System Preferences/Audio" and the volume icon should be grayed out (Another method is is to press "Alt" and perform a right mouse click on the volme icon). OSX don't provide controls for HDMI/Digital output, you have to adjust your volume with the remote control of the TV.
I need to know the content of your S/L/E folder. Navigate to the folder, Select all and copy, open "TextEdit" and in "Composition" perform "Paste and Match Style", save the file and post it.
For the video format you have to try to set the right preferences in "System Preferences/Monitor" (See image), but it is possible you have to adjust something in your TV preferences