Get your meter fixed or borrow one before going on..
From what you say, If you put the "S" wire from the Ignition switch (which you shouldn't do..) to the battery cable, it brings the car to life..in "Start" Only..
If thats the case, the wire that goes from the battery at the solenoid to the "hot at all times" on the Ignition switch..is either not connected or has an open (fuse link) along the wire..
You need to take some voltage readings..
Is this an automatic going in where a manual came out? may have a Clutch over ride involved too.