[Reefer Addict]

Hrm... at the very least I'd do a 10-gallon water change with nitrate readings of 80.
If the rock you added wasn't fully cured before you added it to the tank, it might have created another tank cycle which is causing stress to the fish.

You're also correct that the fish may have arrived ill... a lot of fish are still caught using cyanide, which wreaks havoc in their internal organs. A lot of unexplained fish deaths are due to this.
I'm not sure if that's what your problem was, but I just wanted to let you know that it 'could' have been.
Otherwise, the other advice you've received should point you in the right direction for treatment.
Good luck.

 

[Reefer Addict]

Hrm...
If you've done two 5-gallon changes in the past couple weeks then there's definitely something going on if your nitrate readings are still that high...
Did you happen to test the water before you did any changes? What were the readings before the change?
I usually do a water test right before a change, and a couple of hours after. This usually will tell you if you changed enough water to bring the nitrate levels down significantly. Since you have a fish only tank, it can tolerate a bit higher nitrate level than a reef tank would, but I'd still do whatever it takes to bring those levels down.
Definitely get that skimmer working again... it'll help remove organics before they have a chance to decompose and add to your already high nitrate.
Changing the water twice in a week shouldn't cause much stress in the fish if the new water is at the same temperature and salinity when you add it.
I wouldn't really blame yourself for this problem... chances are you brought a sick fish home from the LFS which contaminated the rest of your tank, or the rock you added may have not been fully cured... I'd put some of the responsibility on the LFS.
These things happen though... it's good to learn right away on how to treat these problems, since there's no guarantee that anything you buy will be entirely healthy.
Hope you're able to get everything in order before anything else perishes.