I wrote a series of articles about the process of creating a 2D platform game which uses AABBs exclusively for collision detection. Here is a link to the article which covered the collision detection and resolution:
There is some free downloadable source-code linked in the article as well which should get you off to a good start
I had actually read several of your other tutorials on my way to finding out how to do this and so far they have been a big help! I hadn't found that particular one so thanks for linking that to me - your blog is a wealth of knowledge.
I think I found out my problem was just how stubborn I was being when it came to implementing a more complicated solution. If I ever saw "collision resolving" or other terminology that I thought to be remotely scary in a tutorial I'd just sort of switch off, I thought there would be an "easier" way to do it. There really wasn't so I started making an engine the proper way and things are starting to slot together and I'm realizing just how simple a physics engine can be. It's been an awesome way of learning and I may post some code here once I get it really smooth.