I think my 2000 Saab 9-3 SE Convertible has an electrical issue

I'm going to go ahead and ask, is your car battery older than 7..the reason I ask is batteries will not accept a charge 10% per year and after 7 years cannot be fully charged~ Also during this time corrosion may have appeared compromising the Cold Cranking Amps and power integrity....so, get a new battery, clean the other end of the black cable, and the 1/0 battery cable going to the engine block, the red wire and it's run to the starter solenoid, make sure that bolt that holds the positive lug onto the solenoid is free of corrosion and you should have no more problems~

The battery was replaced about 18 months ago. Do you think I should replace it and have it checked for the corrosion?

yes. if the battery is new, were golden, just the cable ends got to be wirebrushed clean, especially the ground....seems difficult to explain that semi-conductor devices do not behave themselves when subjected to 'brown' power~...don't forget the engine block too, what we need here is to be able to pull 300 cold cranking amps though there without the wire catchin' fire (hey that rhymes).~

a load tester will provide a destructive 'dead short' for three seconds and see if the battery's okay with it, and starts right up on the next crank...also how much "thirsty" is the battery now after performing this test? accepting 3 amps 6 amps or 15 amps ----very thirsty~ if it doesn't charge up easily, it's a dirtyrotten battery~ ...but yours is a new one and not an issue here~

Probably a dumb question - have you checked the fuses? It might be worth finding out if the three things you mention have a relay in common too?