I have a 1994 GS300 (189,000 miles) also with the same problem BUT with repeated turns of the key in the ignition, it ALWAYS turns over. Been doing this for about 8 months now. I have a new battery, new battery cables and the alternator and starter have been inspected and they pass all tests. The starter was replaced about 5 years ago.
Something in the ignition system isn't working properly. I've taken it to numerous mechanics and they basically don't know what to do since it seems to always turn over when they try it. The last mechanic said: Just replace the starter/solenoid and be done with it! I find it hard to spend $400 to $500 to fix something that is only partly broken.
I guess it depends on your needs...does the car run ok when it does start? Mine still runs great. If it does run ok, then by all means be done with it and get a new starter, This GS300 should go another 150,000 miles!