It's hard to tell at which stage you are right now... there are 2 scenarios:
Scenario #1: Good news!
You already gone through the ANN cycle... the LR already been cured within the 1 month period... all the Ammonia caused by the curing of LR been already converted to Nitrite, then Nitrate. Since the amount of Nitrate is not significant, your test kit is unable to detect it. Job done. Then... a decaying LPS in the tank suddenly raise the Ammonia to 0.25 (which is not a crisis for a relatively new tank). If the Nitrifying Bacteria (N.Bact) already in place residing/multiplying inside your LR, the 0.25 Ammonia will be transformed to Nitrite, then Nitrate in 2 to 3 days. You can run your skimmer as usual (if preferred).
Scenario #2: Not so good news
The ANN cycle has barely begun... something went wrong for the past 1 month... there isn't sufficient N.Bact growth in the system... hence its incapability to convert the 0.25 Ammonia to Nitrite. The 0.25 Ammonia level may stay for a while until your N.Bact is ready to break it down into a less toxic form (Nitrite, then Nitrate). Maybe, try another brand of N.Bact for a change. Off your skimmer totally, let the things rot a bit... higher Ammonia will speed up N.Bact growth anyway... but the bad news is... your tank is not ready for fishes/corals... you probably have to wait for 2 to 3 weeks more.
Scenario #3:
You test kits are not doing its job... possibly expired or somehow contaminated. Do share with us which brand of test kits you using and where/when you bought it.
Before Stocking with LS:
1) Change a huge proportion of the cycling water with properly mixed salt water
2) Test tank water for all major/crucial parameters
3) Adjust all "off the mark" parameters back to acceptable range
4) Run your protein skimmer full force
5) Read more about "how to stock LS" to avoid disappointment
Do keep us updated... we will be with you along the way... but right now, you need to figure out which scenario you are in... perhaps giving us a lot of more information will help... including whatever happened for the past 2 weeks...
Another thing... most protein skimmers will take at least 2 to 3 days to kick-in properly... so turning it "on/off" or tuning it too often for the first few days will stop it from functioning properly.