2001 Ford Escort Escort has intermittent elec. Problem

This 2001 escort will occasionally decide not to start, about once every 2 months or so. The car will drive completely normally, then suddenly, and with no apparent rhyme or reason, when you turn the key there will be nothing, no fuel pump precharge, no solenoid, nothing, as if the battery were disconnected. The first time it did this, after a few minutes it started up and ran fine. The next time, it had to be jumped off, and then ran fine. This last time, it was stone dead except for the trunk light, and the check engine light, which would persist for a few seconds after the switch wass turned back off. We let it sit overnight in this condition, then tried to jump it this morning. Jumping it off restored power to accessories, and caused the solenoid to begin throwing, slowly, but would not turn the starter.
I am concerned that the problem is in the wiring harness considering the weird intermittent nature of the problem, and do not want to start changing expensive components needlessly. The battery was tested on the previous incident, and was fine.