I'm a bit late, but when "live rock" has been allowed to sit dry it is considered dry "base rock". It does not have the bacteria you need to cycle, but it will become live in your tank once you have bacteria.
Live sand and live rock do not usually make for an instant cycle. They merely accelerate the process but inoculating the tank with a starter culture, which then grows rapidly. Otherwise you would have to wait for these things to enter your tank through the air or possibly dormant forms. Your dead rock probably had some organics in it that will help start the cycle by adding ammonia to the water. This is a good thing.
However you should keep up with testing your nitrogen cycle. Your bacteria population is only as large as your feeding will allow. If you aren't feeding the tank ammonia (by feeding the fish etc...) then you have a bacteria population suited to your existing ammonia input. However, as you add biomass your bacteria will need to catch up, growing in number to meet the needs of your ammonia levels (which may be undetectable by most tests). Just add fish slowly to make sure you aren't asking too much from too few bacteria!
Also, I want to mention that ammonia is more of an issue with salt than fresh. Nitrite is often the other way around. I can go into more depth on this subject if you need.