In the long run, not much!
An important thing to consider is that most mathematicians have their highest output when they're relatively young. This certainly isn't true in all cases, but we have to keep in mind that a 45 year old Turing isn't going to be producing as much as a 35 year old Turing.
Outside of that, we could see some facets of computational theory developed slightly earlier (exactly what? take your pick, Turing was one of the founders of the field and dabbled in a lot). But by the 50s to 70s, when a Turing that dies of old age would be working, we've reached the point where it's difficult for one man to make the entire field jump by leaps and bounds. If this was back in the 30s, certainly, but the mid 50s started to be a little too late.
And practical changes would be nil, Turing was a mathematician and computer theoretician, not an engineer, and most of the physical work by the 50s point would be beyond him.
So we might see a few butterflies (Turing's Algorithm instead of Dijkstra's Algorithm?) but I wouldn't think too much more than that.