A bad safety switch would do exactly what you describe, so you may not have to replace the ignition switch...and it's probably an expensive part, so check the safety switches out first.
I have a 1010, but 1030 may be similar in some respects. You need to check the voltage coming into the solenoid from the ignition to see if it's anywhere close to the voltage being delivered from the battery to the starter itself. There may be safety switches between the ignition and the starter solenoid that have failed and which are dropping the voltage or even shorted out.
My 1010 has one at the clutch pedal, and hydro models have them at the range shift lever and at the pto shift lever. In this case, both levers must be in neutral to start the tractor. I realize I'm not describing a 1030, but you get the idea. Trace the wiring, or find someone with a wiring diagram for the 1030, and you'll know where any safety switches are located on your tractor.
The cheap way to test a safety switch is to bypass it with a jumper. If the tractor will then start, you know what the problem is. Be certain the tractor is out of gear and the pto is off, etc, before you try this. There's a reason for the safety switches!
It could be the ignition itself, in which case you'll have to replace it.