Assuming here that you have a single-din radio, probably something like a CR 814... The radio is easy to pull out, using the small vertical handles which pos out of the bottom corners of the radio face. You don't have to disconnect anything to pull the radio out enough to reach the back. Make sure you have the radio security code before you do disconnect anything! Check the connections first, especially ( see Don Foster's post)the antenna. If you want, go to Radio shack or the equivalent, and get a cheap antenna which you can plug into the back of the radio while the radio is pulled out of the dash, but still connected--swap the cheapie antenna for the factory antenna and turn the radio on. If that cures your problem, then follow Don's advice about repair and replacement of the antenna wires/ mast.
Since you apparently have sound in all the speakers, etc, on the AM stations, the problem does not appear to be in the amp or other output portions of the setup.
If you wind up having to take the radio clear out of the dash at some point in the process, take it to a radio repair shop and have them open it and spray the on/off/volume pot with an electronic cleaner while you're at it. This will avoid or delay another annoying problem which would otherwise be likely to start showing up soon--the snap/crackle/pop and intermittent fading of one channel or another after you hit a bump. (not connected to your current problem, just preventative miantenance of a likely one given the age of your radio)
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We have met the enemy and they is us. [Pogo] '99 S70 cop car : Rough Rider tires& suspension, Walmart fog lights, speakers by ebay, ambiance by Pall Mall, trim by Le Duc d'Tape