I have a 97 Accord....Here's the problem,

I had to get my car jumped and it reset the alarm. I had no instructions on how to input the code that I have, but after leaving the car along for about 30 minutes, the car did not re-arm so I figured it would stay that way....until this morning. Once I opened the door, the alarm's blaring. After calling some unhelpful honda service dealers, I received instructions from a helpful service tech. With the code input correctly, the radio turned on and everything seemed to be fine. The car is in the armed mode but when I press the button on my remote, nothing happens. Also when I try to turn the ignition, it will not allow me to turn it fully.

Is this a problem associated with the alarm, the starter (as one unhelpful honda service tech claims), or both?

Thanks