From a NICU nurse in Chicago: I work in a facility where we had over 150 applicants for ONE position. The hospital now hires BSN prepared only. It's a TOUGH market to crack into. If hire new and experience, however you must have that BSN behind your name. This will be true for any magnet hospital. It will NOT do you any harm to get ANY experience you can get. The NICU skills will come to you later, but if you can come in with time management, IV skills, very proficient in tube priming....it will only make your NICU orientation THAT much better and you will feel really good about yourself. I say IV skills even though adults/peds IVs and then baby IVs are vastly different, but even getting a feel for how to hold the angiocath will help!
Stay positive, take your time, get any experience you can get and then try again!