Ignition key will turn but car won't turn on

The key will turn in the ignition. The battery is new. Starter works. Car won't turn on. When I turn the key in the ignition the dash lights will all come on but the car won't start. It usually takes a few tries to turn on. Sometimes it helps to turn the key to the ON position and then apply more pressure to push the key further into the ignition. Before this started happening my wireless entry did not work because the ignition switch would not pop up when I pulled the key out.

My radio would stay on as a result as well and had to be turned off manually. At times my car seems to "shudder" (for lack of a better term) while driving and also while parked or in a stopped position. While the car shudders its turbo gauge rises and declines with each shudder. Can anybody tell me what's wrong with my car and how to fix her?