Radio causes car to die/starting problems

Hi. I have a '93 Honda Civic with 199,000 miles, 4-cyclinder, auto transmission. It has been well-maintained. The last time anything out of the ordinary was done was five years ago, when the battery, timing belt and ignitor unit assembly were all replaced at the same time. I have two problems and am wondering if they are related.

Over the past 2.5 years that I have had the car, I have experienced very intermittent problems with starting the car, probably less than half a dozen. Most of the time it is just sluggish -- chugs and then starts -- but a few days ago I took it out for a short trip and when I tried to start it on my way home, it came on and then immediately died, twice. The third time I depressed the gas pedal right away to keep it going.

The other problem is with the radio, which has a detachable "face." When I attached it the first time (months after I got the car), the car would not start. I thought it was a strange coincidence but didn't try it again. Recently, however, I went through the same thing. I tried attaching the face two or three times in one session. Each time, the engine died as soon as the radio display came on! The former owner used it all the time and didn't have any problems. Do you have any suggestions? Thanks!