Snake in a garage

That's not a very catchy title, but it sums up the day. We spent some time in the back yard inspecting trees. The goal was to find the perfect tree for the kids tree house. John had it narrowed down, but he wanted input from the kids and I. As we finished our backyard tour we headed back inside. Jacob made a pit stop to put something in the garage. He came out yelling excitedly that there was a snake in the garage. If you remember we made a deal that if he could catch a snake he could keep it as a pet. We honestly never though he would get close to a snake, so it seemed like a good plan at the time. Back to today's events. John and I went into the garage to check it out. I ran into the house to get the camera while John attempted to corral the snake. The above two pictures were taken before it managed to climb up one of the shelf supports and hide behind some porcelain tile. We didn't particularly want to move the tile to find it. We just left it alone and came inside to look at snake pictures online. We decided it was most likely a Midland Water snake. Non venomous but an aggressive biter that strikes repeatedly. Okay, that doesn't really sound like a pet to me. Nor does it sound like something I want to startle. After we determined it was probably not poisonous I went back out to the garage to see if it came out of hiding. It was under the mower, and I soon as I attempted to get its picture, it tried to climb the shelf again. John made it out in time to prevent the shelf climb.He injured it with the shovel, but it managed to get behind the stereo and curl up. John used the crow bar to pull it out so he could try to rid our garage of it.Not much was left once John got it out from behind the stereo. Jacob was pretty upset with us. He told me it isn't fair that the snake only got to live a little while. I assured him that Daddy only killed the snake to protect us. Even though it wasn't poisonous, it still bites. He seemed okay with that. Once we got the snake out in the open where we could look a little closer we became less certain about our identification. It could be a grey rat snake. Any ideas?