Guitar Maintenance : My poor old Morgan

[Guybrush]

I have an old neglected Morgan acoustic steel string, all wood. It's gotten beat up over the years, even got a nasty crack in the bottom after a trip on a plane and so on. It hasn't been oiled and the strings haven't been changed for ages.

One of the reasons why I've neglected my poor old Morgan is because the intonation is screwed and having no experience with repairing this kind of damage, I always assumed it would cost a lot. However, I recently thought that I might be able to do this myself.

The problem : It almost seems the neck is too short. If I tune the guitar, I can f.ex play an E. If I play E one octave higher on the same string, it's out of tune. It's pitched lower so you have to pull at the string quite a lot before it sounds right.

The saddle and bone piece (or whatever you call it) on the body are fixed and I doubt there's much I can do with that on my own, but there is of course the truss rod .. Is this problem fixable by adjusting or tightening the truss rod? Is my old Morgan doomed?

Any other suggestions?