Zammy, maybe totally simplify this to try to find what's really happening...
GO back to Blink example. Onboard LED blinks OK??
Then change only that 13 to some other pins. Also try #14 to 19 (The "analog" pins which can also be outputs)..
I've tested quite a few Arduinos with my Test Shield, and have not seen any one pin more that a small amount different...
Let us know...