"Could this be the result of a bad connection between the radio and the antenna?"

I think that's exactly what your problem is. Most likely the antenna wire is loose where it's supposed to plug into the back of the radio.

Removing the radio is easy enough: there are two vertical bands of plastic on either side of the radio. Push them in slightly with a pen or something, and they'll pop out to reveal two finger holds with which to pull the entire radio out of the center console. The antenna wires should be visible as a pair of thick and thin coaxial cables; the thicker one is your main antenna connection, and the thinner one is for the diversity antenna mounted in the rear bumper.

While we're on the subject of radios, now would be a good time to confirm that you have the radio code for this radio, in case you disconnect the power to the radio and thereby lock it up. If the previous owner did not supply you with a radio code card, then you can bring the car to a local dealer and they'll look up the code for you. Normally, the radio code card is supplied with the packet of new owner literature (owner's manual, etc.), so check there first if you don't recall seeing it.
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Jim Rothe, '99 S70 T5M,
http://www.jimrothe.com/volvo/index.html