Hi Dave. Congrats on buying the RR. Because you did not volunteer a lot of info about your starting problem I'm going to assume that you're fairly new to working on these cars. (apology if I'm wrong) There are a lot of possible things that could be causing your starting problem. Basketcase has already started asking a few questions to help you get to the root of things. My initial guess would be a tuning issue. If it hasn't had a tune up in awhile, it would be worthwhile to replace spark plugs, spark plug wires, points (if you still have a points style ignition), distributor cap, recheck the timing, etc... I don't know your age, but I know that a lot of folks that don't have much experience with these older cars are unaware of how much more often they have to be tuned. I'm sure that the guys on this site (like Basketcase) will be glad to help you get to the bottom of what's going on. - More info would be helpful though.
Maybe I didn't read enough into your initial post. You mentioned that it had a new battery and still has times it won't start. Are you saying that at times it doesn't crank over, - even with the new battery? If that's the case, it's obviously a wiring issue or bad starter. The circuit is fairly simple. It's not impossible for the ignition switch to go bad but I don't hear of that as often as other possible problems. There's always the neutral safety switch if you've got an automatic or the wiring as it goes through the firewall. Those bulkhead connectors are known to develop conductivity problems when these cars get old. Usually it's a matter of disassembling, cleaning, and re-assembling the connectors on the engine compartment side. Of course it could be a poor ground that would cause intermittent cranking problems too.
If it is a problem with not cranking over you can narrow the problem down a bit by trying to start the car by jumping the starter solenoid. If it cranks consistently that way the problem isn't in the starter.
