1998 Lexus LS 400 Problems starting

Hi, My car has recently had the following problem: intermittent "clicking" when I try to start the car. Often, after 1, 2, 3 or 4 tries, it will start. We had our mechanic replace the starter - he said the solenoids (sp?) Or the little copper connecters were bad, and instead of replacing the entire starter, he replaced the copper connectors. It's still doing the same thing. It evenutally starts each time, I'm just concerned some day it won't. We have also had trouble with the battery cables and I'm wondering if it may be that those are bad. The battery is new and has been tested. We already paid to have the starter pulled/looked at, and that was about a 6 hour job. Do we do it again, replace the entire started and "hope" that's the problem? Is there a diagnostic which could help determine if it's truly the starter or perhaps just the battery cables? How hard is it to replace battery cables? Is there something else we aren't thinking of?