I hear a noise only inside my car. Sounds like when someone's heart stops beating.... the flatlining noise on a heart machine in the hospital.

Could be your radio noise coming through speakers.

So how would I fix that? Sometimes when I step on the brakes the noise stops.

Why would you leave out such very important piece of information like that out of your question. That noise you hear is the brake pad indicators rubbing against the rotor telling you the pads are getting low time for a brake job. So your next question is why does the noise go away when I apply my brakes and make the noise when I am driving. It all depends on how close or how far away the indicator is from the rotor. Trust me have your brakes checked heard that noise both ways before the brakes are applied and most of the time when brakes are applied.

I took my car to get the brakes checked. I told them about the noise and how when i step on the brake it would stop. They knew exactly what it was. Something about the rotor, uneven calipers and something about a sensor. :-) Would this problem possibly cause my check engine light to come on?

No it would not cause your check engine light come on. Are you talking about the ABS light ?

If I was you I would take it somewhere else to get the brakes checked out. They went you to get calipers and rotors they are trying to get you. Does the vehicle shake when you apply the brakes ? if not you do not need any of what they are trying to sell you.

No it does not shake.

I don't have the money to fix this issue probably for another two or three weeks so I hope this isnt critical :-(

When you hear that noise its not critical that you need to get it done at this very moment but it will not be long. No promises but you may make it that long.

If you have been hearing the noise for awhile now, it's time to get brake pads. Your choice. Pay now and stop or don't stop and pay much more later.