First of all, I know that this has been brought up before. I've looked around on a bunch of different forums, and seen very similar questions asked and answered. However, the solution presented has not availed itself to me. So let me explain real quick.
I'm on Windows 7, and I bought Skyrim on a Steam sale just a little while ago. I just downloaded SKSE for the first time. Downloaded the latest version from the "installer" link. Ran the .exe, and let it create a desktop shortcut. I ran the shortcut, the brief DOS window popped up, and then it skipped straight to the black screen and the Bethesda logo. I tried right-clicking the shortcut and running as administrator. UAC prompted me, I clicked yes, then the same deal. Bethesda logo. I visited the steamapps > common > Skyrim folder, and manually launched the skse_loader.exe (as an administrator) just to cut the shortcut out of it. No dice.
I also tried downloading the .7z version and following the instructions on the readme file for a manual installation. Same deal.
The only real solution I've seen to my problem is to try running SKSE as an administrator, but that's made no difference for me. If someone could point me to an obvious solution and point out my stupidity, I'd be greatly appreciative. I'd love for this to just be something simple and quick to fix.
Again, I apologize for asking the question--it's probably dumb. But thank you in advance to anyone who can help me.