1998 Jaguar XJ8 - 4.0L - 65k mi. - Won't start

Our 1998 XJ8 wouldn't start the other day. I checked the battery and it was bad, so I replaced it. A few days later, it did it again. Turn the key and only the starter solinoid would engage, but would not turn. I replaced the starter and it was fine for another day, but then did it again. We had our mechanic work on it all day, tracing the entire starting circuit, but it started every time for him and he could not find anything wrong at all. It didn't start again the other day when my wife tried it, but it started right away when I tried it with my key. Could it have something to do with the keys or maybe the ignition switch?