If you haven't already then I'd check the state of the engine earth connections both between the chassis and engine and the chassis and the battery earth
they need to be bright and clean and corrosion free
then check the state of the high power fuses ( 40A) in the engine bay fuse box and if the car has a 120A fuse on the battery lead then also check that too
Also check that the alternator is actually charging the battery in the car by taking a battery voltage reading with the engine off then another with the engine running. The 2nd reading should be higher than the 1st and climbing steadily. And also check that the alternator is secure to the engine as this provides the ground for the charging circuit and make sure that the engine / gearbox earth strap is secure and the contacts are clean and bright.
if the alternator appears not to be working - take it to a electrical specialist and ask them to test it as sometimes you can replace just the diode pack and this will repair the alternator without requiring replacement
this sounds like they may have to replace the ignition switch as there a few associated issues and service bulletins with these cars on that area