BMW Z3 from 2000

My Z3 has recently started to act up a bit. Well, actually, when starting the car the "Electronic transmission control module" light (the little gear symbol) has been coming up and staying one, about
every 2 days. I can get it to go off by parking the car, turning off the engine, waiting for several seconds, and then starting the car again. However, I've noticed that when the light is on, there is no noticable difference in anything else. The performance is the same, so I figured it was just an electrical short and decided to go on with my life.
But then things got worse yesterday. Now when I start my car, it struggles a bit to start, giving a "chug... chug... chug, chug" sound before starting yesterday. Then this morning it did it again, but when the car started, the on board computer (i.e. the clock display), warned that the outside temperature is +24F. Considering that I live in Texas and park my car in an unairconditioned garage that is actually more near 85F, something is really wrong. It normally only comes on in the middle of winter when the outside temp is in the low 30s or below.
When I got to work this morning, I parked my car, and then decided to test it out. I started it and it again had the same problem: a labored start and then an even more wild outside temperature warning: -15F. All of these problems (transmission light, starting, and temperature warning) seem like they have one thing in common: electricity. I've checked the battery, as it has the little charge indicator on it, and it is a solid bright green, indicating a full charge.
So what could it be? What should I look at or try next? I want to get a good idea as to what is wrong before I take it into the shop. The labored start has me worried more than anything else, but the car has yet to fail to start. It just acts like it is having to work extra hard to accomplish the ignition.
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Have you replaced the battery yet. My M was acting funny whenthe battery was low. No problems since I replaced the bat.
Al
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