Well... you've actually covered two lessons here!
The first is that the shrimp everyone talks about cycling with is dead to start with! You're just looking for something from the ocean that will basically rot in your tank to make ammonia. That ammonia source will then start your cycle. Sooo... the fact that your shrimp is now dead is not really a problem. Except for the shrimp.
If you don't have test kits for ammonia, nitrites, and nitrates, go out and buy them now. As the shrimp rots, you'll see the ammonia levels rise. When you get 2 or 3 ppm
ammonia, then you can safely take the shrimp out. (Or what's left of it.) As you ammonia levels rise, you'll start seeing nitrites show up. When the nitrites peak and start declining, your ammonia levels should pretty much be gone. At this point, you should start to see nitrates going up. Eventually, after 4-6 weeks, you'll have 0 ammonia, 0 nitrites, and some amount of nitrates. Your tank is now officially cycled!
Nothing will make the nitrates go away execpt for water changes with aged, mixed saltwater. Once you do several water changes to get your nitrates down between 5-10ppm, then your tank is ready for inhabitants.
The second lesson you've learned is how NOT to acclimate your livestock when you add them to your tank! You need to slowly acclimate them over an hour or so, depending on how different (salinity, pH) the water is that they're coming from versus your tank water. You can find an article on acclimation, as well as other good "just starting" articles here...
Regarding adding live rock, what kind of filtration do you have on the tank right now? When creating the cycle, you're creating a population of bacteria that will convert ammonia/nitrites into nitrates. That bacterial needs a place to live, which normally would be either in a wet/dry filter, a biowheel, or in live rock and sand. If you have none of that, you'll want to add the live rock now since the bacteria needs a place to call home.