Q: Car starts but dies a few seconds later. If I give it any amount of throttle (once it has started) it kills the engine

I have a 1984 porche 944. It has worked like a charm for the past 5 years but last week things turned for the worst. It just got really cold here in utah and my car is now struggling to get running. More specifically, the car turns over and starts just fine but dies immediately after starting. If I keep cranking the engine over and keep trying to start it eventually it does start and run just fine. Also, when it has finally succesfully started without stalling, I have to let it sit and idle for about 10 minutes before doing any actual driving. If I try to give it any sort of throttle during that initial idling period it just kills the engine. But like I mentioned earlier, if I do let it idle and warm up, eventually I can drive it like normal without any problems. If the engine is warmed up and I turn it off, it can sit for several minute

I am fairly knowledgeable in the field of automotive but am no mechanic nor an expert. I would appreciate some professional advice.

My car has 200000 miles.
My car has a manual transmission.