That is an incredibly frustrating problem, and you've already done some serious troubleshooting by replacing the push button and the module. The message on the dashboard is the key here. It's not a generic message; it's a specific instruction from the car's computer, and it points directly to the steering lock system.
The "wiggle steering
wheel" message is telling you that the steering
wheel's electronic lock, which is an anti-theft feature, has engaged and won't disengage. The lock is a little pin that slides into a hole on the steering column to hold it in place. The car won't start until that pin is fully retracted. The reason it tells you to wiggle the
wheel is to take pressure off the lock, allowing it to retract.
The fact that you've already tried this and it's not working suggests that the steering
wheel lock module itself is the problem. This is a very common issue on many vehicles with a push-button start, including your 2009 Genesis. The module can fail internally, and no amount of wiggling will get it to work. It can sometimes be an intermittent problem that gets worse over time, which sounds like what's happening to you.
Unfortunately, it sounds like you have already replaced the part that is most likely to be at fault. However, there are a few other things that could be causing this. The wiring harness to the steering lock module could be damaged, or there could be a bad connection. You can try to visually inspect the wiring for any signs of damage.
Another thing to check is the car's battery. If the battery is weak, it may not have enough power to activate the steering lock, which can cause the car to not start. You said that you've done all sorts of things, so you may have already checked this, but it's worth a second look, especially if you have an older battery.
A proper
diagnostic scan is really your only option at this point. A standard code reader won't be able to read the codes from the steering lock module, so you'll need to take it to a shop with a professional
scanner that can communicate with the car's body control module. They can tell you exactly what the issue is.
This is not a simple problem, and you've already gone above and beyond what most people would do. It's time to get a professional to look at it and tell you for sure what's going on.