2005 Hyundai Elantra erratic rough idle

The place to start is by reading and recording the diagnostic fault codes. Many auto parts stores will do that for you for free.

One possible cause of a high idle is a vacuum leak, usually in a vacuum hose. Besides that, any change in idle speed proves the idle speed motor is working so forget about that. The throttle position sensor tells the Engine Computer throttle position, direction of change, rate of change, when you're at idle, and when you're at wide-open-throttle. It doesn't have anything to do with idle speed, so forget that.

We don't get involved with repair costs because there's way too many variables, plus, we don't even know the cause yet of the problem. The best we can do is offer some suggestions and alternatives.

A dirty idle air control valve can cause an unstable idle speed, but that will not occur suddenly like you described, and it won't have as much affect as what you listed. The valve opens up to allow more air in, and at the same time the Engine Computer commands more fuel. Those two things raise idle speed. A dirty idle air control valve will restrict the amount of additional air and the complaint will be an idle speed that is too low, often resulting in stalling when approaching a stop sign, and / or hard starting.

You're describing the opposite condition where way too much extra air is getting in resulting in an idle speed that's too high. I'd be looking for a cracked or disconnected vacuum hose first. Sometimes you can hear them hissing when the engine is running.

The next step is to connect a scanner to view live data and see what the Engine Computer is telling the valve to do. If it is telling the valve to close completely, it's because it sees that idle speed is too high, and it's trying to bring it down, but without success. If you see the computer is requesting a higher idle speed, you need to look at the other sensor readings to see which one is in error.