Cell towers can detect the receive power of any given cell phone on their network. If you just hacked your cell phone to use high transmit strength, they would know and could kick you off their network.

I can imagine that you could rig your cell phone (or another device) to transmit at high power to jam the connection, but the FCC would have something to say about it. If you're caught, I'd expect civil and criminal reprisals...

Stiff fines. If suddenly the only signal the tower's picking up is yours, it doesn't take too long to figure out who is responsible.

Prepaid phone, bought with cash, and left in a public place?

If you keep it up it can be triangulated, I suppose. Other than that, the tower would have to shift everyone to a different frequency.