I'll assume you've double-checked and tried all the controls and made sure that there aren't any really dumb things you've overlooked. You said you tried the squelch, so I assume that means in both directions.
One possibility is the mic switch, element, or broken mic/cord wire. Are there any signs the CB is stuck in tx mode even with your mike switch open? If the radio is stuck in tx mode, you won't hear anything.
If someone else has a Cobra mic, you can try substituting that to see if it works. I don't know the age of your radio, but broken wires in mic cords are pretty common from what I've read.
I doubt its your problem, but I have a Midland and it came with the wrong mic because they switched wiring at some point and it exhibited similar symptoms.
You should be able to receive something with nothing more than a wire stuck into the center pin on the antenna connector in the back so even a crappy antenna should let you hear something if only noise. There is always some noise as far as I can tell. Can you connect your CB to someone else's antenna to see if it works. Unless you're pretty sure it isn't stuck in tx mode, I wouldn't advise the wire in the center pin for fear you'd have a reall high SWR and burn out the tx transistor(s).
If you can't get it to work with a different antenna and a different mic, I'd say its time to take it into a local shop. They should be able to tell you real quick if its the radio or the mic.