Damn it. Well that is definitely a ScriptHookDotNet failure since the Tilde isn't working and you have no ScriptHookDotNet.log file.
At this point I'd say you have a fully functioning .NET 4.0 installation that you don't need to touch again. It's working.
The issue is trying to figure out why ScriptHookDotNet doesn't work. I'm not the author of that so I don't have the source code to it. I could probably decompile the thing but that debugging of that should be provided by Hazard and I don't know if he provides that or not.
I'll take a look at his readme and web link and see if there's anything we could use to get debug info from it.
For the hell of it did you try installing this from his site:
Note that is a x86 version. If you are using x64 you could also try:
Also I'm not sure what OS you're running, nor where the game is actually installed. What happens if you run the game As Administrator? If it's Vista or 7, the program files folder is considered a protected folder and does require permissions for certain actions so ti's at-least worth trying to load it as admin and see if ScriptHookDotNet finally loads or not.
Title 7 update:
Also I just saw your request for title 7 update in your message up thre doh. 1 sec let me find it and I'll update this.
I got it from here. Ignore the fact it says russion/jap. It's stupid. It works for english and should probably just say all. But anywah, see if this is the one you are using?