I guess it was too scared to move
Don't bet on it.
That sounds like a very sick deer. Probably very close to death. If the deer didn't spook till you touched it - that means that it's brain was simply not functioning correctly. When you touched it - you initiated a "flight response" -an almost completly reflexive reaction. The fact that it ran away by no means its OK - in fact - what you describe sounds like a severe infection - possibly of the brain - or effecting the brain.
Sorry
FH