Jason McBrien wrote:
  What about magnetostrictive delay line memory? Output
could be a typewriter
 rigged up to solenoids, though I'm not sure when solenoids were invented -
 I've found companies that have been producing them since 1918. They're easy
 enough to build. 
Post WWI seems to be about the right age, for computers could have been built.
I even have the right USE ... computing for building bigger ships for the Navy.
Forget why computers were developed after WWII, this is historical fiction.