I just bought Skyrim on my Acer 2009 pc, and I opened it up and it was a little slow which is fine with me.
Then, I downloaded a few mods off steam like Realistic Ice and Water, and Better Grass, etc. But now when I open Skyrim it goes to game screen (with mountain in background), and I hit the start button or whatever it is and it just closes.

Is it the mods doing it?

Most likely, yes. Can you post your load order, and your PC specs (specifically, the processor, RAM, and Processor)? We might be able to help you trouble-shoot from there, but it sounds like you might just not have a powerful enough PC to run Skyrim on higher settings.