Hello Laura,
Sorry to hear of the problem and I know how you feel - we do expect cars to be reliable, but cars of the Stilo's age and complexity frequently aren't.
Start with something simple - check that the battery leads are tight on the battery terminals. The battery should be under a cover that you can remove with either a standard flat screwdriver or a 10mm spanner if someone's put different bolts in there. You'll need the 10mm spanner anyway for the terminals.
Going further, the big question is whether the engine fault light (yellow outline of an engine shape) is on. If it flickered or came on while the engine was running, there's a good chance that reading the fault codes will help with finding the cause. For example, an intermittent ignition coil failure, or the air pressure sensor mentioned earlier in this thread (which you did well to find!)
I always say that everyone who owns a Stilo needs a diagnostic cable (ELM327 type) and the
MultiECUScan software on their laptop, as it's the only way that an owner can really figure out what's going on. Otherwise, you are going to be at the mercy of specialist garages who have this equipment. Cable and software costs under £75. This is a major development since this thread was started about six years ago - the software simply wasn't available at a reasonable cost back then.
I do have sympathy
I've owned about 30 Italian cars and have only ever broken down (as in, failed to get home) in two - one was 10 years ago, an ex-scrapyard Uno that belonged to a friend, and the second time was a month ago in my Stilo when its airflow meter suddenly died. I could possibly have driven it home if I'd unplugged the faulty airflow meter (ECU applies default settings) but I didn't think to try that.
Hope this helps in some way... with my airflow meter replaced and split cooling system hose replaced, I'm expecting reliability to return
-Alex